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