Hi. I've search for the Shop FLIGHT Magazine item, and the shop search says:

This item can be found in these locations: Achievement Prize

So I clicked and it send me to the achievement page. How do I found which achievement I need to complete to get that specific item? Thank you.

You may want to bookmark Subetalodge, it usually has extra information on items like that.

The Achievement for that item was part of a plot, I think, and has been retired. It is no longer possible to get that achievement, so it's also no longer possible to get the item as a prize. However, you can still buy the item from user shops or maybe check the trades now and then.

The Shop Search isn't very clear on things like that. I've had similar problems with items marked as Battle Loot, but then you have to ask around the forums or search for the item on Subetalodge to find out what opponent drops the item. And unless you know to do that, I can see how that would be confusing and frustrating. Subeta has many positive qualities, but it's not very newbie-friendly imo.