We do not currently know of any adverbs for acclimatize.
Using available adjectives, one could potentially construct nonstandard adverbs such as acclimatably, acclimatedly, acclimatisably, acclimatisationally, acclimatizably, acclimatizationally, acclimatorily, acclimatingly, acclimatisingly or acclimatisedly.
Note, however, that these words will not generally be contained within standard English language lexicons.