If you want to remove the tile from the backer board, I would get a chissle and remove one tile, then the rest will come off easy because you have leverage.
Watch the eyes for flying tile.
The best and easiest way is to remove the tile with the backer board. Usually when removing each tile one by one, you will damage the backer board and cause more problems.
Its like changing the oil in your car and not the filter. I would remove the tile and backer board.
Then once the stuff is gone and the studs are showing. Attach either cementious backer board or green board and then attach new tiles. Be sure to use water proof mastic and also water proof grout.
Do this, apply the mastic and then the tiles. Wait one day before grouting. Some people grout immediately. If this happens, the grout will seal the tile and not allow the mastic to cure and dry. Very bad thing to do.
Then after one day, grout the area and then wait two days before using the shower and on the third day apply silicon sealer. This will seal out the water and keep algea from growing.