Here is the full list of all 17 Giana Sisters: Twisted Dreams - there are Director's Cut achievements worth 1,000 gamerscore.
Land on an owl while twirling
Collect a yellow gem while dashing
Unlock the power to warp your dreams.
Collect a red gem while twirling
Jump or dash onto three owls without touching the ground
Defeat Hansel + Gretel
Defeat Octor Freud
Defeat Gurglewocky
Defeat the Owlverlord in on normal difficulty or higher
Bounce off a falling turtle
Use a spiky box like a trampoline
Collect all gems in the game (except Extra levels)
Obtain five stars in all levels in hard mode (except Extra levels)
Unlock Hardcore Mode
Unlock Über Hardcore Mode
Obtain a trophy in all Time Attack levels
Obtain a trophy in all Score Attack levels