Rent a vibrating floor sander from a home improvement store or a tool rental company. Do not install a sanding pad on the bottom of it, since you are simply loosening the parquet tiles.
Plug the electrical cord into the wall and turn the machine on. Push it over the parquet floor using a slow pace to vibrate the tile loose from the underlying glue. Turn the machine off, unplug it and move it out of the room.
Walk to the edge of the floor and angle the flat edge of a spade or floor scraper under the edge of the parquet. Push with force to detach as many tiles as possible.
Continue pushing the flat blade under the flooring using force to pry the tiles up off the subfloor. Most of the tiles should lift easily since the vibrating tool breaks the bond of the glue.
Sweep all of the removed tiles into a pile using a sturdy push broom and then shovel them into a large trash can for disposal.
Fill a bucket with 1 gallon of warm water and pour in 1 to 2 tbsp. of a liquid dish soap. Insert a long-handled scrub brush into the bucket and apply the mixture to the floor until all areas of adhesive are wet.
Scrub the floor vigorously with the broom to detach the glue once the water softens it.
Mop the floor with fresh water to remove all of the adhesive particles from the floor.