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Creating a new tile tub surround is not as difficult as you might think, but there are some important points to consider. Instead of hanging the tile on the old existing drywall, you should replace it with cement backer board of equal thickness.
Then all the seams between the pieces of backer board and the existing drywall should be taped with fiberglass mesh tape and coated with thin-set adhesive to prevent cracking. Once that’s dry the seams should again be coated with a waterproof compound to keep all moisture out of the walls.
When you start setting the tiles, remember to work from a level line—don’t just trust that the tub ledge is level. The wall tiles should also overlap the seam between backer board and drywall slightly, so no one sees the transition.