Here is the full list of all 20 DuckTales: Remastered achievements. It takes around 15-20 hours to unlock all of the achievements on Windows.
Unlock all art in the Gallery
Beat game on Extreme difficulty
Beat game on Hard
Enter either underground section of Amazon and climb up the other side using only the pogo jump.
Collect All the Heart Containers on Easy or Medium difficulty
Defeat 5 enemies under the effect of 1 magic coin
Get to the secret gyro area in the clouds
Buy art in the gallery
Get back what Magica stole
Defeat 5 enemies in a row with pogo jump without touching the ground
Collect the Green Cheese of Longevity
Collect the Lost Crown of Ghengis Khan
Collect $10,000,000
Collect the Giant Diamond of Inner Earth
Collect the Coin of the Lost Realm
Collect the Sceptre of the Incan King
Scrooge doesn't take kindly to being swindled by statues
Eat some of Mrs Beakleys delicious treats
Dive into the Money Bin
Defeat Big Time Beagle using your noggin, and his