Do note Achilles tendonitis can be a chronic situation if it doesn't heal properly. Need proper strengthening and avoid aggravation. Avoid complete long period of rest coz if so long liao, and it is still painful, then it's likely a situation of tendinosis liao, i.e. chronic and will never heal and further degradation as one age in nothing is changed.
I mentioned before. If you intend to use running for strengthening the tendon, use high heel dropped shoes, avoid soft cushioning and choose firm mid sole. Avoid long mileage run, choose shorter distance like 500m to 1km to start. But do it everyday to avoid long period of complete rest. Increase distance gradually.
I had hardly run anything more than 5km during the strengthening of tendon for self rehab. Basically high frequency + low volume is better than Low frequency +High volume for rehab.
And the rest of the day, walking with zero drop slipper is best as it stretches the tendon to load it. But the intensity and repetition is low and will not aggravate it like long distance running. But than again avoid long walks like hiking more than 10km without rest, it's a zero drop slipper after all which mean your tendon is extremely stretched, high load. Stick to nearby walk of 1km to 2km, rest and repeat it to go home.
Why avoid complete rest. Rest encourage tendinosis, i.e the degradation of tendon. Tendon area has poor blood supply, movement or stretching the tendon in the only way to encourage nutrients to get to the tendon for repair. Just like our knees cap, no blood supply there for repair, but movement will encourage some form of repair.