Here is the full list of all 27 Titan Souls achievements.
Beat Hard Mode
Kill the Skull Titan as it spins
Kill the Eye Cube while pulling back the arrow
Open the first Sealed Gate
???
Cut all the vines off the Plant Titan
Beat the Game
Knock yourself out in the battle for the Titan Soul
Kill the Knight after destroying all pillars
Produce 50 coins in the Chest fight
Succumb to the effect of spores for 30 seconds total
Open the second Sealed Gate
Finish in under 10 seconds...
Destroy all icebergs
Drop a bomb on the Lava Blob Titan's head
Kill the Sludge titan with no more possible divisions
Slay a Titan
Beat the game in under 20 minutes
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 Brain with a flaming arrow
Kill the Rolling Titan in under 5 seconds
Remove all teeth from the Mountain Titan then kill it
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