I have not had this event, sadly.
First of all, do you need to defeat them? The other empires would seem to be toast. Can't you go grab all the resource anomalies?
If you do need to beat them, can you not just research logistics and get fleets of your own? For that matter, if their ships are poorly weaponed with missiles and you have great missile defense, one or two of your ships might take out entire fleets w/o problem.