Here is the full list of all 17 Giana Sisters: Twisted Dreams - there are Director's Cut achievements worth 1,000 gamerscore.
Defeat Hansel + Gretel
Jump or dash onto three owls without touching the ground
Collect a red gem while twirling
Collect a yellow gem while dashing
Unlock the power to warp your dreams.
Defeat Octor Freud
Defeat Gurglewocky
Defeat the Owlverlord in on normal difficulty or higher
Land on an owl while twirling
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