I know a fair bit about their actions in the Mediterranean world, Syria, and Mesopotamia, but have heard very little about the other half of the Empire.
What we know about the contacts between the east and the Achaemenid Empire is extremely limited due to the absence of any survivng historical references in either Achaemenid Persia or the many states of the Indian subcontinent.
What is likely is that there were trading relations with India and that Elephants, used against Alexander and eventually under the successor states of Alexander, the Parthians, and the Sasanians, were traded or given as tribute to the court. These either would have originated from Sri Lanka, as the case of certain Sasanian elephants, or from trading relations among the Indian states themselves.
Since Elephants were clearly used by the Achaemenid, it can be hypothesised that other items and tribute came in and that the Achaemenids could have recruited troops to guard their eastern frontiers. I'm not sure of any sources that list Indians fighting with Alexander prior to his invasion of the subcontient.
Unfortunately, until something comes up that expands this field further most of what historians can do is hypothesise what actually occurred.
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