Stanley makes a small ripping bar called a 'Wonder Bar'. It's a mini crowbar. Put at the joint btn the concrete and the tack strip under a nail. Whack it with the hammer to wedge it under the strip. Then pry upward. The tacks are likely only 5/8" long and smooth shanked, so they'll pop out with relative ease once you get a little leverage this way.
I did a 9x12 room like this in about 10 minutes.