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