Here is the full list of all 17 Alex Kidd in Miracle World DX trophies - there are 2 bronze, 5 silver, 9 gold and 1 platinum.
All trophies have been awarded.
Free Egle at Radaxian Castle.
Pet the sad dog.
Defeat Ox.
Defeat Grizzly Bear and Funky Monkey.
Defeat Gooseka in the Radaxian Castle
Defeat Chokkina in The City of Radaxian
Defeat Parplin in Nibana Lowlands
Get the telepathic ball in the "Mt.Kave" level.
Talk to all the NPC's in the game.
Finish the game without buying items in the shops.
Get all the collectibles.
Discover the secret island.
Defeat Janken the Great.
Clear the "Namui Lake" level without shooting with the peticopter.
Complete the main story.
Win the Jankenpon tournament.