When should we recite Ashtakshara mantra? Should it be while reciting Acarya thanian or during sandhyavandanam? How many times should we chant? I have heard its glory and benefits through Vidwan-s but need clarification on how many times and when to chant it.

Ashtakshara japam should be done during sandhyavandanam, also all three times. It is enough that you can chant them during sandhyavandanam and apart from this time there is no need to do it separately. You can refer Ahnika grantham or ask your preceptor for chanting the same.