If the Achilles heel mission is the one I think it is (you are attacking a Dread Lord planet?) I just made a ton of small ships with big weapons and military starbases to make them stronger.
The Dreadlords get 1 - 2 ships at a time, but you can have many more. They can take out 1-2 ships at a time, but you can take them out. You can easily make 12 ships and keep killing them as you send in wave after wave of troop transports (to kill all of 10 guys)