How does achilles tendonitis occur in gymnastics?

Any injury of this type comes from overuse. The area is subject to consistent stress that creates small or micro trauma to the tendon. This trauma never heals properly and it creates further stress on that area of the tendon which leads to more swelling and tenderness. The way to stop this is to develop enough strength in the tendon to stop this micro trauma from happening. There is an exercise called the 180's. When your leg is healed start this movement. Stand with the of the feet over the edge of a step or other area where the heels can hang completely down. Raise up both heels as high as they can go. Then take the right foot off the step and slowly lower the left heel down until it reaches the bottom of its range of motion. Now using the right foot replace it on the step and raise that heel up as high as it will go while having the left foot off the step. Do that 15 times with the left foot and then switch the routine to the right foot and do 15. Each week add another set of 15 until you have reached the point where a total of 180 repetitions are being done. This will develop enough strength to stop this problem.