Here is the full list of all 31 Pixel Piracy achievements.
Capture an enemy ship
Accept a bounty quest
Have at least 5 poop on your ship
Horke the Flatulent poops
Have a seagull poop on your ship
Visit an island with no town
Set sail for the first time
Visit a tavern
Pick a fight with a legendary pirate
Defeat a legendary pirate
One of your pirates dies while using Kaboom
Kill a hobo
Capture an animal to be your pet
Die for the first time
Plunder an enemy ship
Find a treasure chest and open it
Have a pirate turn hostile due to low morale
Add a pirate flag to your ship
Check out the Main Menu credits
Have both Vitali Kirpu and Alexander Poysky on your ship
Have 5 of your crewmates wear diapers at the same time
Capture 50 animals
Defeat all the Legendary pirate ships
Have 10 or more pirates on your crew
Kill a total of 1000 enemies
Dig up 10 buried treasure chests
Unearth an epic buried treasure
Loot a total of 10000 gold
Visit a panda island
Find a stranded hobo
What was that? Did we just travel to hell?