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