One thing that might help riding with an Achilles problem is moving your cleats back, or your feet forward.
This shortens the lever arm on the foot, and the calf/Achilles strain. It's not going to be a miracle, but it will help somewhat. Also, ride lower gears because the strain is proportional to the pedal force you're applying. Higher cadence in lower gears will help both the quads and Achilles.
Then, and this is the most important ----- LISTEN TO YOUR BODY ----- and be conscious of how the affected areas feel, while not masking anything with drugs.
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