I've got more than one character (4 at level cap plus one in progress to be precise). They don't all have the same achievements. Most of them are missing many of the seasonal events items because I hadn't created the character yet.

You don't need any of the items you listed to play an alt. Not every character needs to have every item.

If you want an achievement reward on a character badly enough, earn the achievement. There are very few achievements in this game that require extreme effort.

If you want the mogstation items (including previous seasonal event items) on the character that badly, then buy them. They aren't that expensive when they're something you're going to actively use on a regular basis.

It's amazing how much stuff you discover you really don't need when the game doesn't just hand them to you for free.