Here is the full list of all 26 Leviathan's Sword achievements.
Finish the tutorial
Save your 1st crewmate
Save your 2nd crewmate
Save your 3th crewmate
Defeat the first boss * 10
Have a total of 200 coins
Pick up 3 booze items in 1 run
Complete a run without getting hit
Beat 3 daily challenges
Beat 10 daily challenges
100 enemies fell into a hole
Beat the game with The Captain
Beat the game with The Hunter
Beat the game with Lifeless
Squish 100 tiny cockroaches by rolling over them
Beat the first 3 bosses on challenge mode with Captain
Beat the first 3 bosses on challenge mode with Hunter
Beat the first 3 bosses on challenge mode with Lifeless
Kill 100 enemies with cannonballs
Bounce a bomb 5 times
Beat the first 3 bosses on challenge mode with Ivan
Beat the game with Ivan