Here is the full list of all 48 Spider: Rite of the Shrouded Moon achievements.
Climb to the roof of Mansion South.
Eat two insects with one tackle.
Complete a web with 6+ sides without touching the ground.
Trap all bugs, eat none.
Build a web while maintaining a 5x web multiplier.
Collect an Atlas Moth.
Collect a Coleophora Moth.
Collect a Death's Head Moth.
Collect a Luna Moth.
Collect a SwallowTail Butterfly.
Earn Scholar or better rank in 30 levels.
Tackle a hornet after eating 10 bugs in a combo.
Eat an insect exactly at midnight.
Eat 33 fireflies.
Swat 50 houseflies.
Tackle a hornet while jumping from one web to another.
Create a six-sided web.
Secret Achievement
Juggle a cricket or grasshopper three times.
Attain rank of Knight in 30 levels.
Earn 50,000 points in less than 15 seconds.
Earn 32,500 points consuming only marshflies.
Max out both of your multipliers.
Trap 3 clusterflies in a 9-sided web.
Discover 5 ways to die.
Spin 64 4-sided webs.
Attain rank of Knight for the first time.
Tackle an insect just before dying of hunger.
Trap a snakefly in a 7-sided web.
Investigate the Captain's Quarters.
Find something hidden in the Vault.
Discover a secret in the Study.
Witness an event in the Laboratory.
Build an 8-sided web that isn't strong.
Finish an incomplete secret society symbol.
Tackle a dragonfly into a hornet.
Tackle all 5 gnats in a cluster in one jump.
Trap 10 insects in a 10-sided web.
Complete a level in under thirty seconds.
Play the game under all 4 conditions.
Enter a code that is valid but expired.
Eat 3 angry hornets without taking any damage.