Here is the full list of all 16 Alex Kidd in Miracle World DX achievements.
Defeat Parplin in Nibana Lowlands
Defeat Chokkina in The City of Radaxian
Defeat Gooseka in the Radaxian Castle
Free Egle
Defeat Grizzly Bear and Funky Monkey
Obtain the Telepathy Ball
Defeat Ox
Beat peticopter level without shooting.
Discover the secret island
Defeat Janken The Great
Speak with everyone in the game
Beat the game without buying any item in shops
Pet the sad doggy
Get all collectibles
Complete the main story
Beat the Jankenpon Tournament