Ditto to glennjanie,
You want to set tile on a SOLID backing. If any of your tiles are loose, cracked grout lines, etc. you can bet you have gotten moisture back behind the tiles at some point.
Rip it out to the studs. This way you can pull out the tub and replace it as well. If the tub is on an exterior wall, you will be able to insulate there as well. (assuming an older house w/ minimal or no insulation to begin with.)
Staple on tar paper for vapor barier
Screw on cement board w/ appropriate screws
Tape the corners w/ fiberglass
Now you're ready to snap a couple starting lines and away you go w/ the tile.
It will be a mess and take twice as long as you thought, but after done, you will KNOW that the job is done well.