How can I cure Achilles tendonites?

Curing the. Inflammation is key. Whether by medications, rest, or injections, the inflammation is the big issue. If you are used to using nsaids, that can help, but clear with physician. You may need stronger things like steroid injections and rest. Once the inflammation is stopped, stretching, strengthening are key, of both the achilles and the plantar fascia.
You can do this: Because tendons have a poor blood supply, healing is going to take longer than you expect. Inflammation is part of the healing process, so be careful about taking or doing anything that will reduce the healing process. You must stay off of it as much as possible and do not do anything that will cause the calf to over used. Apply moist heat to the area and under use, not over use. Docs can do more.
Achilles tendonitis. Curing achilles tendonitis can take up to 3- 6 weeks for some patients. I recommend many excellent treatments that are simple to do. Getting an exam will give you the best diagnosis and treatment plan that you need. Best wishes!