Is there a way to see what achievements have item prizes?

yes, but not easily.

Go to personal->Achievements

Then look for achievements with little ⭐, click the star. Most will have Titles. A few have items.

A good example to look at is the filled wardrobe achievement under Wardrobe. It has a bunch of item prizes.

You can also go to SubetaLodge, Achievement Prize Search. Which will list all the items that come from achievements. Two problems with the list, you need to click the items individually to see what achievement they come from (its in item notes) and there is no indication if the achievement is retired or still available.

Thank you for the answer!