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