Here is the full list of all 27 Titan Souls achievements.
Open the first Sealed Gate
Kill the Eye Cube while pulling back the arrow
Slay a Titan
Open the second Sealed Gate
Beat the game in under 20 minutes
Beat the Game
???
Beat the game in Iron Mode
Beat the game in Iron Mode with New Game+
Beat the game without rolling rolling rolling (in No Roll mode)
Kill the Sludge titan with no more possible divisions
Beat Hard Mode
Kill the Brain with a flaming arrow
Cut all the vines off the Plant Titan
Succumb to the effect of spores for 30 seconds total
Kill the Knight after destroying all pillars
Produce 50 coins in the Chest fight
Kill the Rolling Titan in under 5 seconds
Drop a bomb on the Lava Blob Titan's head
Kill the Skull Titan as it spins
Finish in under 10 seconds...
Remove all teeth from the Mountain Titan then kill it
Destroy all icebergs
Knock yourself out in the battle for the Titan Soul
Kill the Broken Statue Titan while pulling back the arrow
Trigger the Guardian's switches with the wrong hands and kill it
Slay all Titans in Iron Mode