Sky Lynx needs a lot more weapons to win this fight. That's not in the spirit of a fantasy battle though.
Sky Lynx has one possible way of winning. He could do a kamikaze attack and slam into Omega at hypersonic speed, preferably with a hold full of heavy cargo in his shuttle cargo bay. That might be enough to neutralise Omega. Sky Lynx could survive by transferring his brain(s) into a temporary backup body. His body would be completely scrapped but that could be replaced in time.