The most significant power level difference is when you go against the first Akee sector boss with the geno class ship so here's a list of things I found helpful and prioritized them:

Stealth Fighters:
Try to avoid the stealth fighters getting destroyed and being patched until a sector boss battle, as they'll get rinsed by the enemy stealth ships pretty quickly if they are patched.

Additional Squadron Dock/Heat Capacitor:
You should prioritize an additional Squadron Dock above all else while going through the first sector of Chapter 3, it's costly (300 scrap) but the first sector boss has 4 squadron docks, I was always on a losing defensive battle with only the initial two squadron docks when I came to the sector boss. Next the Heat Capacitor upgrade should be bought at least a couple times as Akee ships generally have an weapon that adds a lot of heat to systems.

Crowd Control Weapons:
The invisibility projector the ship starts with is not great, so just sell it. Get some good RNG or cheap MK1 crowd control weapons from stores (weapons that have no effect on battleship hull like the Plasma Nuke) as the stealth fighters the Geno Class ship starts with should be adequate enough to deal with the battleship. A great weapon for this situation is the Sub Zero Gun (any MK) as the AI generally bunches the stealth ships together so the moment they uncloak you can freeze more than one of them at a time.

Omniforge:
You should ignore it for the first sector unless you got really great RNG with scrap and just go for the route with the most scrap (route with the most planets to launch missions). Mainly due to the expensive squadron dock and heat capacitor upgrades previously mentioned.

Proximity Repair:
Try to get a crewmember with proximity repair when going this route, it'll help significantly more to shore up your defenses than any other hull ability.

Battle Strategy:
The only real weakness of the Akee sector bosses (as the Geno Class Ship) I found to be was that they have a really long dock recovery time so when the battle starts I deployed my stealth ships right next to my battleship and wait for them. If you manage to get a good cruiser, do the corner strategy with that cruiser and two other stealth fighters, as the projectile from the cruisers does hit multiple enemies if they're clumped up on the same tile, so this combined with the Sub Zero gun is really effective.

Once the enemy stealth ships are destroyed, recall the fighters and deploy drones to go at the battleship (as they're the fastest moving unit) it's alright if they're destroyed you need to do the most damage possible to the enemy ship. At this point, crowd control weapons should be charged and help you defeat the next wave of enemies, you need to become good at guessing where the enemy stealth ships route is going to be when they're deployed so that you can disrupt their cloak, additionally, they may go after the drones attacking their ship which also does it.

Then just rinse and repeat this strategy until victory.

After the first sector, get your heat capacity and hull points bars to max and hopefully find better stuff. The RNG with events in the sector might make it so where you have to attempt it a few times to get it.

By the way, I love this game enough that this is the first guide my lazy butt decided to write on Steam, so if anything is wrong (outside of my potentially awful english) in this guide let me know and I'll edit it...