Here is the full list of all 72 APICO achievements.
The base game contains 39 achievements, and there are 3 DLC packs containing 33 achievements.
Catch your first butterfly species
Catch half of all the butterfly species
Catch all of the butterfly species
Fully repopulate a butterfly species
Fully repopulate half of all the butterfly species
Fully repopulate all of the butterfly species
Discover your first new solitary bee species
Discover half of all solitary bees species
Discover all the solitary bee species
Fully repopulate a solitary bee species
Fully repopulate half of all the solitary bee species
Fully repopulate all the solitary bee species
Catch something in your butterfly net you didn't expect
Collect all the bee-sides
Net a butterfly that's not quite finished yet...
Discover a solitary bee that doesn't look quite right...
Catch yourself your first fish
Complete half of the Captain's Board
Complete all of the Captain's Board
Discover all bumblebee variants of fish
Catch a... fish? I think?
Refine sludge to find a little treat
Refine sludge to find all 6 little treats
Restore the red ruby coral reef
Restore the green emerald coral reef
Restore the yellow topaz coral reef
Dive down into the depths of the ocean...
Clean up one of the patches of sludges on the sea floor
Clean up all patches of sludge on the sea floor
Descend, and descend again...
Commune with an emmisary...
Walk through a doorway to another world
Light up all the obelisks