Here is the full list of all 17 Giana Sisters: Twisted Dreams - there are Director's Cut achievements worth 1,000 gamerscore.
Unlock Über Hardcore Mode
Obtain a trophy in all Score Attack levels
Obtain a trophy in all Time Attack levels
Obtain five stars in all levels in hard mode (except Extra levels)
Collect all gems in the game (except Extra levels)
Unlock Hardcore Mode
Defeat the Owlverlord in on normal difficulty or higher
Defeat Gurglewocky
Defeat Octor Freud
Bounce off a falling turtle
Use a spiky box like a trampoline
Defeat Hansel + Gretel
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