Cessna 152 Flight instructor reported a wind shear encounter on short final resulted in a temporary loss of control and tail strike during an attempted go around.

Narrative

On a flight training operation with a presolo student pilot; we departed Runway XX to fly the traffic pattern. The METAR and ASOS corroborated the winds were 250@12G18kt. I requested a pilot report before takeoff and was told '+/-5kts'; which was within my personal minimums. Windshear was not forecast or expected. There was no AIRMET present for windshear; and the winds aloft were stable in direction and velocity. My student and I elected to fly a no-flap approach to allow for more available thrust in the event of a go around or drop on final. We turned final at 85kts and flew 80kts to the numbers. Published approach speed in the aircraft is 60kts; so we were well above the recommended gust factor addition. As my student began the round out phase of the approach (literally just beginning to bring the nose up; the nose never reached the horizon); roughly 15-20ft above the runway; we started floating out of our seats. The rate of descent became higher than I've ever seen in two years of instructing; though I did not have time to view the VSI. I initiated a go-around; applying full power and bringing the nose up. The left main gear impacted the runway hard; and I heard a loud pop. We taxied the airplane back to the tie down and inspected. The tail tie down was smacked hard; bent backwards; indicating a tail strike. I cannot think of something I could have done differently. The rate of descent was so high; that had we not pitched the nose up and added full power; we would have impacted the ground at an unacceptable rate. Two aircraft in the pattern also executed two separate go arounds. There was no stall indication; and the aircraft did not feel similar to that of an aircraft in a stall.