Here is the full list of all 12 Giana Sisters: Twisted Dreams - Director's Cut trophies - there are 9 bronze, 2 silver and 1 gold.
Defeat Gurglewocky
Defeat Octor Freud
Use a spiky box like a trampoline
Unlock Hardcore Mode
Defeat Hansel and Gretel
Unlock the power to warp your dreams.
Collect a red gem while twirling
Jump or dash onto three owls without touching the ground
Obtain five stars in all levels in hard mode (except Extra levels)
Unlock Über Hardcore Mode
Obtain a trophy in all Time Attack levels
Obtain a trophy in all Score Attack levels