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