First timer with a Bathroom Wall Question

First time homeowner here.

The bathroom wall in the home I bought had some crappy tileboard covering the bottom half of the wall. I pulled it off and realized that the wall had been tiled before. Instead of properly scraping off the old Tile adhesive, they just covered it with the crappy tileboard.

I want to redo this wall, preferably by tiling the bottom half. My question is, do I need to completely scrape all of the old adhesive off before I can put something new over it? I have scraped off a section of it, and it is pretty time consuming, and some of it does not come off that well. I have seen mention of something called skinning the wall, where you could cover it with something instead of removing it all, but I do not know about that.

If I do need to remove all the old tile adhesive, do you have any recommendations for something to help with that? Home depot does not have any tile adhesive remover(which surprised me) and the ones online seem to have varied reviews.

Also would you recommend patching all of the small holes where the old tileboard was riveted into the walls before tiling? Or would the tiles just cover that with no issue.
Pictures below, any help is appreciated. Thank you.

I would just cover it with 1/4" backer board and tile it with a trim at the the top.

You should be able to thinset over and 1/4rnd. on the top.

Thanks for the replies.

Snoonyb, what do you mean by 1/4 rnd on the top? Some kind of 1/4 inch molding where the tile stops you mean?

Yes, depending upon the trim available from the tile mfg. a 1/4 rnd. provides a transition to the wall plain.

Assuming you have drywall and not plaster/lath construction, it might be worth the time and effort to just replace the drywall and start fresh.

It is a plaster/lath construction, not drywall.

Still trying to figure if I just want to drywall over everything, or tile it.

Local handyman gave me an estimate of $850 to drywall the whole bathroom(minus the shower area)