Just got to Round 10 a second time:
This time I was a bit unfortunate, I knew I couldn't win.
I actually had a really good setup against most things, it was just a bit weak against anything with 4 shields, and completely ineffective against anything with 4 shields and a defense drone
I used the Kestral Type A. I had 3 shields, a shield recharge augmenter, and a MK2 defensive drone. Unfortunately my weapons, though very cost effective, were quite weak (comparatively). I kept the Artemis and MK2 Burst Cannon I started with, but I added a Pike Cannon to the mix. The strategy was to hit the shield module with a missile, further damage it with a few burst cannon shots, then when an opening appeared, rip the enemy's hull apart with the Pike Cannon. The strategy relied quite a bit on luck, as if the missile or the burst cannon shots missed, the shields wouldn't go down. If the shields didn't go down, the Pike Cannon was useless. Fortunately I had a powerful defensive setup, so I had plenty of time for my luck to finally "kick in". Unfortunately, against 4 shields and a defense drone, the strategy was impossible to execute because the missile got shot down, and neither of my other two weapons were powerful enough to break the shields ;p
I'll have to do some variation of that which can actually penetrate the shields in the future. I find that on normal, with a "brute force" strategy, you tend to be very low on scrap, so the weapons you may need to beat the end-game either come before you can afford them, or even if you can afford them you can't afford the sheer number of weapon slots necessary to even use them.