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