You can soften construction adhesive with a heat gun and use a putty knife scraper to get most of the material removed. Once you have reduced the remainder to a very thin layer you can use any of a number of commercial adhesive removers or even acetone to further soften and allow the remainder to be scraped and wiped away.
Care must be taken with adequate personal protection and make sure plenty of ventilation is provided when using chemicals like acetone or other noxious / volatile solvents.
In the end since there is a good possibility that the old tile job was originally poorly installed and had leaks and bad backer. So your best bet is likely to be complete removal of all the old tile, backer and/or underlying drywall down to the bare studs. Then you can start a new install with the best modern tile install methods and materials. This also gives you the opportunity to inspect and replace any framing, insulation, wiring, plumbing and backing for any shelves or other things needing to be secured to the wall after the new tile is installed.