Getting a foothold in the starting islandsSpoiler
Rather than start at the obvious place, start at the tiny southern island with the turret. It's really hard to take later on, and packed with goodies.
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Take the mine and the energy pod with your HQ and plop two omnis for the rest. You will probably lose the mine momentarily, but your omnis will take it back if they have the power from the energy pod.
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You then have just enough time to grab the floating mine immediately left, then move north to the mine at the center of the three "starting" islands. Don't worry if you lose the floating mine.
If your HQ gets damaged, you can move it over the island and let it heal before retreating back down south.
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Build 3 omnis at this center island as soon as your omnis have fully taken that small first island, abandoning it. When the 3 omnis are built, have them fly down and convert that spawner. I lost the island shortly after, but kept the spawner, which is the real goal at the moment, so don't worry if you lose the island. If you can keep this island, getting those turrets functional will really help give you some breathing room.
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Now you have some freedom on how you take the rest of the starting islands, but getting those two amp gems is a huge help. Easiest route is probably to swoop to the bottom, then around clockwise to grab the two floating mines, then the amp gem before going back for the spawner (with the help of the destroyer.) Might be different depending on where the enemy ships are coming from.
Once the starting islands are secure, the game is a lot less sketchy, since those turrets and spawners will help protect you. You have a couple islands you could do next.
Might be good time to dip into Rock Burners for a bit to clear out that scattered land around the center mine. Better to have more struc, plus more free aim of the spawner.
Sideways CSpoiler
The sideways C to the north is probably the next easiest and just involves using an amp gem on your HQ to mine the first mire spawner, shooting away the structure with omnis, then timing a couple omni flights to take over the gun. Alternatively, you could grab the mine first, but it's sometimes hard to hold on to till that spawner is defeated. A gem in mine cannons helps keep the particulate away from that mine while it lathes the spawner.
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Next up is the one to the east with the lathe pickup. Take out the two mire spawners with your HQ, then throw all of your omnis at the rest until you can establish a foothold, using destroyers to block particulate. Extended range helps you build omnis closer to the island, and flying over it with ships while your omnis are flying in helps to take shots from the enemy mines so your omnis don't get hit. Emitter control helps here, too. This one is kind of a bitch to hold on to, so once you get the items, you can abandon it. Although burning out the rock for defense lets you hold onto the mines pretty much forever. Might as well flip that emitter directly NE once you've taken the whole island, too.
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Send all of your omnis in waves to first claim the two turrets. Once those are claimed, just land your omnis and let them do the rest. Maybe land near that mine so you can claim it. The ships should be easy to defeat once you have the island.
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Using the newly acquired tank, you can land on the NW island and take that over. Using that island you should be able to grab the first spawner, and work your way east to grab the next island and its goodies and kill the ship spawners, then head south. With the help of the spawner, you should be able to have enough firepower to grab the small center left island, which basically shores up your victory of this area.
South center island with big round ship.
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This one is a bit of a bitch. Use the tank you just acquired to build omnis at the south side, and send them to land, till you can take over the island. Took me a bunch of tries till I got it. After that it's pretty easy to mop up.
Far SE island
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This one definitely requires an outside the box trick because I wasn't able to win with a frontal attack. The way to take this is by warping your HQ in twice to grab that floating mine at the south. After that, it's just a matter of throwing omnis at all of the spawners till you can grab control of the island.
Final Area
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The trick here is that you need to burn away the two small islands in the center of the broken island, so you can use the spawners offensively. You can grab the last grabber by ship bombing the rotating ship. With two grabbers, you should be able to throw enough particles at the big island, to allow your omnis to land, and take it over. Then just mop up.