Here's just to use as a key for the map once constructed based off of my knowledge and experience. These are normally where I find these bugs the most

Grasshopper - Any regular grass or dirt tiles excluding Snowtown
(Black) Ladybugs - Onnet Town, Eastern Li Forest/Yorkton Border, Belle Isle
Mantises - Outskirts of Swamptown near the bridge, Belle Isle, Onnet Town, Eastern Li Forest, Balamb, Yorkton, Castle, Oasis
Dragonflies - Swamptown, Balamb
Fireflies - Onnet Forest (possibly Deadwood or whatever it's been renamed. I haven't been on to check), 'Bees Knees'
Spiders - Onnet Forest (possibly Deadwood)
Worms - N/A
Karner/Blue Morpho - 'Bees Knees', Oasis (these are only where I've found most of them; they are scattered elsewhere)
Monarch - Graal City, MoD (scattered else where)
Ringlet - Onnet, Li's Forest, Southern Swamptown/Deadwood (scattered elsewhere), MoD, Belle Isle, Mountainous regions
Small Blue - Southern Swamptown/Deadwood, Mountainious Regions
Clouded Yellow - MoD, Space between Swamptown and Graal City (scattered elsewhere)
Emperor - Onnet, MoD, Belle Isle (scattered elsewhere)
Peacock - Oasis (scattered elsewhere)
Argias - Oasis (scattered elsewhere)
Great White - Onnet, MoD, Graal City, Li's Forest, Mountainious regions, Swamptown
Tiger - To my knowledge, Li's forest and Oasis (I haven't found them elsewhere)
Green Hairstreak - Belle Isle, Swamp Town, Railroad Tracks (outside), Deadwood, Southern Montanious regions
Swallowtail - Graal City, MoD, Belle Isle, Li's Forest
Pillbug - Railroad Tracks and Caves

Let me know if I missed any.