Here is the full list of all 25 Giana Sisters: Twisted Dreams achievements.
Land on an owl while twirling
Unlock Cosmonaut Comrade from the SpeedRunners game by completing a race in three different Dream Rush levels
Complete a Dream Rush race
Unlock the power to warp your dreams
Defeat Hansel and Gretel
Defeat Octor Freud
Defeat Gurglewocky
Collect a red gem while twirling
Collect a yellow gem while dashing
Jump or dash onto three owls without touching the ground
Bounce off a falling turtle
Use a spiky box like a trampoline
Avoid spikes by ducking
Collect all gems in the game
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
Complete the first world in Über Hardcore Mode
Complete the second world in Über Hardcore Mode
Complete the game in Über Hardcore Mode
Have a human win a race against bots in a Dream Rush level
Have a human win a race against bots in two different Dream Rush levels
Have a human win a race against bots in three different Dream Rush levels