Update!
I might as well include the other quests for those who want it.

For those who don't have a clue on the quests that were recently released with the new town Destiny, here is a guide. This guide also has theprevious quests!

Special Boots

Spoiler

Area: Boot Camp
Head to the boot camp and speak to the man at the counter. He says his boss isn't here yet. Click on every boot and talk to the guy again. He will let you pick one of your choice. They all cost 5000 gralats.

Price:
5000 gralats

Boots:
Hover Boots: Lets you hover in mid-air
Splash Boots: Leaves a trail of splashing water behind you.
Moon Boots: Makes you jump when you walk
Opposite Boots: Makes you go the opposite way
Ice Boots: Makes you slip as if you were on ice.

Coin Quest

Spoiler

Head to the church in Destiny. The church is on the west side of destiny. Once there, go through the broken window on the left side of the door. Go and kill the Lizard. Once killed, walk up to the giant boulder and use a bomb on it. Talk to the priest on the other side for a coin.

Reward;
Coin

The coin always lands on tails

Key & Bomb Quest

Spoiler

In one of the houses to the right of the enterance to destiny, there is a gnome. keep talking to him until he asks you a question. say yes. head to onnet town and go to the locked house. go into your rat morph and go through the hole in the door. Kill every rat, destroy every bush and grass. After you finish, you get the deed. Head to the bank and walk up to the counter. Equip the deed and use it. the banker will offer a price. say no to th first time and yes to the other. Make sure you have money on you or the deed will be empty. Head back to the gnome and talk to him. The waiting game is in session. Wait 6 hours and go to the house you got the deed from. talk to the gnome and he will give you a different type of lantern. Head to destiny and into those yellow towers. open every chest and move the boxes from the blocked chests. check every room and chest and you will get the key. Go to the stairs with cobwebs and equip the new lantern. the cobweb will burn and you can go up. open the chest with the key and BAM! You got a new bomb

Legendary Bow

Spoiler

Go into the cave that is below the enterance to Destiny. Head to the right all the way to a metal door. Equip your new coin and use it. the door will open. Head in. You will see a bow for sale. The price is 10000 gralats. Pretty darn expensive. Head to the Fletchery and use an arrow to hit the target behind the desk. the side doors will open. Go in and exchange your broken legendary bow for the real deal

Treasure Maps

Spoiler

Head back to the room you bought the Legendary bow from. There should be a Bag on a wooden counter. buy it for 400 gralats. You can now go map hunting

How to get maps;
Maps can be obtained by digging, killing bandits, pyrats, baddies, and in chests in destiny.
Some say they found maps while looting. I don't know if it works but give it a try!

FireFighter Hat

Spoiler

Go to the fire department, go up and talk to the guy with a beard. He and his men will head to a cave. follow them to the smaller cave that has lizards in them. Once in the cave, take the stairs and go into the next cave. you will find the firefighters there. Go up and bomb the broken wall. The firefighters will leave. Follow them back to the department and take to the captain for a firefighter hat

Scarf Quest

Spoiler

The scarf quest unlocks a mask shop in Master Li's Woods, where you can get multiple masks for 2500 gralats each.
You need a BURGER before you start, so buy one from Burger Refuge. Now go to North Graal/MoD Town, and just follow the path straight north. Enter the cave and follow through the door (or small waterfall if you prefer), get in the water and swim to right into next room. You'll find a half-dead dude named Monty. Feed Monty your burger and he will give you CAT FOOD.
Now do an "unstuck me". From Sister Gertrude's, walk east to the outdoor bar called The Joint. Give your tasty cat food to Morris, whose kitty is stuck in the tree. He will use the cat food to lure Mr. Chunnitz down from the tree and will give you a RAG.
In MoD Town, theres a small shack between where Red Dragon Inn and Black Orchid were moved. Give the rag to Raphael. He will dust off his boxes and give you a MIRROR.
Now Unstick and make your way over to Chris Kill 'Em's (the mansion in the cave next to Angel Clan). In the bathroom, Undine, the self proclaimed Queen of Graal, will swap your mirror for a SHIRT.
Get on a horse, because now you gotta get to York Town. Enter the bar next to Alan who sells the phoenix. Present the shirt before Jackman, who will grant you with a lovely box of MATCHES.
Unstick and go to Sara Rei's house, where SNC Guild House used to be. Uh oh! The door's locked... but theres a crack in the roof. Jump off the side of the cliff to crash through poor Sara's roof. Your crash landing somehow manages to blow out Sara's candles and she gets ticked off at you. Give her the matches so she can relight the candles. She gives you a PAINT BRUSH.
Now go to where the old Master Li's Sparring Dojo USED to be. In the middle of the forest, there is a painter named Hyto. Surrender the paint brush and gain a BOOK.
Now head on to the Battle Arena's Library. There's a fellow there named Everest who has been searching for a particular book ever since the library opened. It just so happens you have the exact book he's looking for!*Now your new friend gives you FISHING LINE.
Now go see our old buddy Toll Guy at the south end of the bridge. He will tell you a long and very boring story. Basically he got bored with gambling with RPS, so he wants to take up the hobby of fishing. Fork over the string to him. Congratulations you won a SCARF.
After obtaining the scarf, a new shop will appear in the trees next to Hyto, our painting buddy in Master Li's Forest. Apparently, the shop owner was not ready to open... so you have to wait 30 minutes and come back. Why did you need a scarf for that? Don't ask me. However there are rumors that the quest is still incomplete and the scarf may be used in the future.

This quest Info was obtained from http://graakass.wikia.com/wiki/Quests
I am too lazy to write all that

Archery Tournament Quest

Spoiler

This quest requires you to have 500 gralats first, in order to buy a ticket. So, first go to the Archery Building in Onnet Town, and buy a ticket from the counter for 500 gralats. This will allow lifetime access to the Archery minigame. The object of the game is to score points by shooting arrows at targets; you will have a time limit to shoot as many as you can. You don't even need arrows, you will be given some to use for the game, but aren't allowed to keep them afterwords. You will need to get a score of at least 2000 to complete the quest, so get in queue! A few important tips: Don't shoot the targets with an X on them, you will lose points. Try to shoot the targets in the center, this is called a 'bulls-eye', and also try to get multiple 'bulls-eyes' in a row to get chain bonuses; this is necessary to get at least 2000 points. Once you get a score of 2000 the NPC at the archery room will hand you a key. Use this key in the first room where you bought your ticket to unlock the chest. Inside you will find a quiver that lets you hold 200 arrows instead of 100.

Flipper Quest

Spoiler

The flipper quest is an extension of the scarf quest. To obtain the flippers, follow these steps:

First, make sure you have 500 gralats. Then, go visit the fishing guard at Graal Bridge and pay him the cash. Once all the conversation is over and he's done fishing, go to the railroad cave above York Town. Then head north into the waterfall cave. Then stand in the middle of the light blue circle and use the fish. BAM! you got a flipper

Butterfly Net Quest

Spoiler

Head to MoD town and go into the house that looks like a tree. Talk to the guy on the bed and he gives you a net. Have fun catching bugs!

Shovel Quest

Spoiler

In this short quest, you while acquire the shovel tool! You can use this to dig in the dirt and hopefully find worms. It is possible to sell these to the witch in swamp town just like you would with normal bugs, as described in the Butterfly Net Quest, however they are only worth 1 gralat each, and may be used in a rumored fishing feature later on, so save them. Anyway, start by going to MoD town. You will want to go to the small lake with the waterfall south of the tree house. Go inside the center of the waterfall and you will find yourself inside a small cave. Talk to the NPC inside and he will challenge you to a race. Win the race and he will give you the shovel.

Assault on Pyrat Bay Quest

Spoiler

This quest can be done every 24 hours for repeating rewards! It is very simply, travel to Pyrat Bay and start killing pyrats. They commonly drop eyepatches among other things which you should pick up. Once you have 75 of them, click on the guard by the gate on the southern part of York Town. Click 'Finish Quest' and you will have completed Pyrat Assault Quest and have earned yourself 1000 gralats! Come back each day to do it again for another 1000 gralats.

Big City Quest

Spoiler

First off, travel to the newly discovered island using the boat on the west side of Delta Island. Also, it is important to note that you need the flippers from the Flipper Quest and a shovel to complete this quest. So, first go into the water, then travel around the island until you find a circular group of rocks. You will fall into a cavern. Leave there and you will be up on the cliffs. Go until you find an old tree and jump into it; it should be a straight down fall, and there are rock there to mark where you should jump. You will find a skeleton nearby in this new cave. Dig around with your shovel until you find a preserved note, leave the cave and bring this to the archaeologists south of the entrance you make by leaving. You must equip it and show it to him for this to work. He will run off to investigate the area. Go back to where you found the note and talk to the head archaeologist, he will give you a translation book. This allows you to buy things from the totem pole shop, furniture shop, and the fan shop. Next, go to the Chief's house on the northeast part of the island, be sure to have your shovel equipped. He will tell you he once lost a necklace and wants you to find it, he will give you a hint as to where it is; this is different for each player. Dig around the area he tells you until you find his necklace and then bring it back to him. He will give you a bear hat. Next, go south of his house and enter the hut east of the fan shop and talk to the person in there with the bear hat you got on. He will tell you the way to harness the spirit of the bear's pelt and you will get the Bear Morph.

Rat Morph Quest

Spoiler

Head to Onnet forest located north of onnet town. There are three paths in each area. try to get to the end without getting warped to the enterance. If you do, try again. You get to the end when you find a witch. Talk to her for the rat morph!

If I missed out a quest or have some misleading info here, just give a reply and I will fix them. This was written from the top of my head.
Thanks for reading.  

nobody has figured out how to go to the pyramid  

Probably an update will come for an item that wieghs you down to get to the pyramid  

Posted by Sardon

nobody has figured out how to go to the pyramid

i went there very 1st day.  

Thanks! But does anyone know what a bandit key is used for? I got one a while ago and still don't know what it's for.  

Posted by JayC

Thanks! But does anyone know what a bandit key is used for? I got one a while ago and still don't know what it's for.

Opens a chest in cave to get a bomb  

Posted by Shadow M.

For those who don't have a clue on the quests that were recently released with the new town Destiny, here is a guide.

Special Boots

Spoiler

Area: Boot Camp
Head to the boot camp and speak to the man at the counter. He says his boss isn't here yet. Click on every boot and talk to the guy again. He will let you pick one of your choice. They all cost 5000 gralats.

Price:
5000 gralats

Boots:
Hover Boots: Lets you hover in mid-air
Splash Boots: Leaves a trail of splashing water behind you.
Moon Boots: Makes you jump when you walk
Opposite Boots: Makes you go the opposite way
Ice Boots: Makes you slip as if you were on ice.

Coin Quest

Spoiler

Head to the church in Destiny. The church is on the west side of destiny. Once there, go through the broken window on the left side of the door. Go and kill the Lizard. Once killed, walk up to the giant boulder and use a bomb on it. Talk to the priest on the other side for a coin.

Reward;
Coin

The coin always lands on tails

Key & Bomb Quest

Spoiler

In one of the houses to the right of the enterance to destiny, there is a gnome. keep talking to him until he asks you a question. say yes. head to onnet town and go to the locked house. go into your rat morph and go through the hole in the door. Kill every rat, destroy every bush and grass. After you finish, you get the deed. Head to the bank and walk up to the counter. Equip the deed and use it. the banker will offer a price. say no to th first time and yes to the other. Make sure you have money on you or the deed will be empty. Head back to the gnome and talk to him. The waiting game is in session. Wait 6 hours and go to the house you got the deed from. talk to the gnome and he will give you a different type of lantern. Head to destiny and into those yellow towers. open every chest and move the boxes from the blocked chests. check every room and chest and you will get the key. Go to the stairs with cobwebs and equip the new lantern. the cobweb will burn and you can go up. open the chest with the key and BAM! You got a new bomb

Legendary Bow

Spoiler

Go into the cave that is below the enterance to Destiny. Head to the right all the way to a metal door. Equip your new coin and use it. the door will open. Head in. You will see a bow for sale. The price is 10000 gralats. Pretty darn expensive. Head to the Fletchery and use an arrow to hit the target behind the desk. the side doors will open. Go in and exchange your broken legendary bow for the real deal

Treasure Maps

Spoiler

Head back to the room you bought the Legendary bow from. There should be a Bag on a wooden counter. buy it for 400 gralats. You can now go map hunting

How to get maps;
Maps can be obtained by digging, killing bandits, pyrats (After you finish the daily quest), baddies, and in chests in destiny.
Some say they found maps while looting. I don't know if it works but give it a try!

FireFighter Hat

Spoiler

Go to the fire department, go up and talk to the guy with a beard. He and his men will head to a cave. follow them to the smaller cave that has lizards in them. Once in the cave, take the stairs and go into the next cave. you will find the firefighters there. Go up and bomb the broken wall. The firefighters will leave. Follow them back to the department and take to the captain for a firefighter hat

If I missed out a quest or have some misleading info here, just give a reply and I will fix them. This was written from the top of my head.
Thanks for reading.

thank you for this  

Posted by Shadow M.

Maps can be obtained by digging, killing bandits, pyrats (After you finish the daily quest), baddies, and in chests in destiny.
Some say they found maps while looting. I don't know if it works but give it a try!

OMG, I LOVE YOU!!  

You don't need to buy map satchel? The decipher guy gives you one.  

I got a treasure map from a pyrat before daily quest was done, maybe it was bugged for me or it is just a low chance.  

Thanx for making this thread

Posted by Bryan*

Opens a chest in cave to get a bomb

which cave? :3  

You forgot the dragon quest.  

Posted by Droid

You don't need to buy map satchel? The decipher guy gives you one.

This has since been fixed. When Destiny was first released there were some leftover debugging scripts running that was giving players the Satchel for free.  

You can still get maps from Pyrats whilst doing the daily quest. I got two from doing it, it's a false rumor you can't obtain them in the midst of it.  

Posted by Dusty

This has since been fixed. When Destiny was first released there were some leftover debugging scripts running that was giving players the Satchel for free.

Do the free satchels work properly?