Pry the edge or corner of the damaged tile using screw driver or scissor. Try to find the loose corner then pry upward. Only when a single tile is removed you can easily remove others by using scratcher.
Give a little cut at the corner of the tiles using knife or any sharp object, then use the heat gun to provide heat at the bottom of the tiles so that the glue used during sticking it is diluted and then remove the tiles using scratcher.
While removing the tiles wear gloves and use adhesive dissolver to dissolve the sticky material. And wearing gloves will safeguard your hands from heat gun, scratcher and the glue.
Work systematically throughout the room. After removing you will surely feel like mission accomplished. After using the remover solution, wash the underlying floor with water and soap.