Alex Kidd in Miracle World DX

Important notes -
The achievement does not unlock until after you complete the game.
You can use infinite lives to get this achievement.
You can not speak to NPCs whilst on the motorbike or in the pedicopter, so it is best to not purchase them on Marble Plains or The Village of Namui respectively.
You don't have to speak to the shop keepers for this achievement.
I don't know if the dog counts towards this, but the dog is next to another NPC, gives an achievement itself and gives a collectable too, so no reason not to quickly pet the best boy.

1. Mt. Eternal, visible from the start.
2. Mt. Eternal, about half way down the mountain.

3. Marble Plains, just after the shop and first scorpion. Do not buy the motorbike.
4. Marble Plains, after the 3rd pyramid of breakable block, laying down.

5. The Village of Namui, just a little walk past the shop. Do not buy the Pedicopter.
6. The Village of Namui, on a ledge just up right of the [?] block. The Dog is also here.

7. The Radaxian Castle, in the first room with multiple exits.
8. The Radaxian Castle, from first Knight, go through bottom right exit, down ladder, down another ladder and Gamer Knight is right there. Alternative path from first Knight, down pit, down ladder, right exit and there's Gamer Knight
9. The Radaxian Castle, from Gamer Knight, left exit, down ladder, and there's Lantern Knight.
10. The Radaxian Castle, From Lantern Knight, right exit, right again and you'll you'll find the Big Helmeted Knight in the top right corner.


If TA ever updates my captures successfully I'll add the screenshots I intended to add to this guide.