Tips:
You have to starve the big ship of energy. It may look like all your shooting isn't doing much but once its energy tanks go empty it starts repairing a lot slower, and firing slower too. You can get to this point fairly easily even while the enemy has all its energy mines.
The hatchet ships are good for cutting off parts. Park the long side right at the edge of the map. You have to find good locations to do this.
The top left is where the large ship's bridge is. It's much better defended than the other corners. Leave it for last.
If you cut one of the non-bridge corners off on both sides, it'll explode because it's no longer connected. That's how you get rid of them. If that blows up your hatchet ships too, well, they're disposable. Build more. Put a gem in move and build speed, too. If the big ship grows back too much, cut it again.
Once you blow up a corner, take over its energy mine and don't let go of it. This considerably weakens the big ship because it can no longer refuel from it, and you get much more energy *and* more room to build your own ships in.
Once you control the non-bridge corners, the bridge basically just crumples because it has no energy. Mop it up and win.