Getting to Asia is not straightforward from BOS as there are no non-stop flights to any Asian hubs. But you should definitely be able to get to PUS with 2 stops. If you're willing to fly from JFK, you can get to PUS in 1 stop. If you're willing to fly into ICN, you can get there from BOS in 1 stop. I'm not sure whether the latter is a good idea or not.

I assume you're flying coach. Doing a search on Orbitz for a random week in March shows the cheapest ticket at $1239 right now. Routing is BOS-SFO on UA, SFO-ICN on SQ, overnight in ICN, then ICN-PUS on OZ. Consolidators may have better fares. PM me if you want the name of the consolidator that I typically use.