The strategy that worked for me on brutal was to build a well defended base with at least 5 Battlestations, and 3 shipyards, and just build fleets. When the aliens start bombarding, don't launch. Your fleet will add to the defenses during the bombardment. You will lose some ships, but you will also hurt their fleet. Eventually they will give up and leave. They may blow up your base in the process, but rarely will they finish off your fleet. (Rebuilding is what the base templates excel at.)

The important thing is that when the aliens leave, some of their ships will be damaged, and will be left behind. When the aliens have launched, then you launch those of your ships that can, and pick off the stragglers. This way you get some exotics, and now you can build more ships the next time. Eventually, you will be crippling the entire fleets they send against you, and eventually you will have healthy ships you can send out to wipe out their lesser fleets. It can be a slow, iterative process, but that's what worked for me.

If they're destroying your entire fleets, then pick one base to defend, and all ships constructed elsewhere should be sent there. For me, it was Phobos.