Here is the full list of all 28 Titan Souls trophies - there are 12 bronze, 8 silver, 7 gold and 1 platinum.
Collect all Trophies
Slay all Titans in Iron Mode
Beat the game in under 20 minutes
Beat the game in Iron Mode with Hard Mode active
Beat the game in Iron Mode
Beat the game in Hard Mode
Beat the game without rolling rolling rolling (in No Roll mode)
See the Truth
Beat the game
Knock yourself out in the battle for the Titan Soul
Trigger the Guardian's switches with the opposite hands and kill it
Cut all the vines off the plant Titan
Kill the knight after destroying all pillars
Produce 50 coins in the chest fight
Destroy all icebergs
Open the second sealed gate
Succumb to the effect of spores for 30 seconds total
Drop a bomb on the lava blob Titan's head
Kill the skull Titan as it spins
Kill the rolling Titan in under 5 seconds
Remove all teeth from the mountain Titan then kill it
Finish in under 10 seconds...
Open the first sealed gate
Kill the broken statue Titan while pulling back the arrow
Kill the brain with a flaming arrow
Kill the eye cube while pulling back the arrow
Slay a Titan
Kill the sludge Titan with no more possible divisions