Xbox – Transfer Walking Dead 2 Save from XBox 360 to XBox One

As far as I know, this is not an official bug hence there is no official solution/fix for this. Many people encounter this issue, but many people not.
Here is a discussion of those people faced this problem and some fix.
Some solutions may or may not work.
So I wish you luck with one of the solutions mentioned in the link.

this is kind of dependant on what the game does. some games have specific wallpapers for achievements while others use a simple image.

The custom backgrounds was part of the November 2014 update which was around the same time Far Cry 4 launched, so it's understandable they did not have specific backgrounds. It's also a third party game, so I'm not sure that they wanted to put in the extra work in creating images for each achievement.

You can set a custom background to whatever you want, it doesn't have to be an achievement. You can read up on a guide and get a template for custom backgrounds here.

but... to answer your question: no, there is no way to use 360 style achievements on the XB1