Enemy with 2 shield layers in Sector 3.
I'm in Fed A with only my level 2 Artillery Cannon and the starting Burst Laser. I have 2 layers of shields (level 5, so an added buffer against damage) and level 4 Engines with fully upgraded helm but only semi-upgraded engine room guy.
Fine. Target shield room.
He has a fast-charging Heavy Laser and a missile launcher. Both weapons fire before my Burst Laser can charge.
First laser shot misses, then the missile hits my O2 (upgraded, fortunately, so still operational).
My return fire: Hit, hit, miss just as I'm about to do hull damage.
Next volley.
His first laser shot hits (not that it matters), then so does the missile. Empty room, but it's next to the Artillery Beam and it set a fire. Vent 4 rooms to shut the flames down, and breathe a sigh of relief.
My return fire: Miss, hit, hit. Fine. Let my hit 3 times in a row, PLEASE?
Next volley.
Laser misses, then missile hits. Again. This time damaging my shield room (lucky it's only 1 damage).
My shots are hit, miss, hit.
Next volley
First, MY ARTILLERY BEAM. Which fires into a room near one corner of the enemy ship, but moves out into the corner, only hitting 2 rooms, one of which is his drone room that only provides a single defense drone (and isn't damaged enough to disable that drone even if I cared to kill it) and the other is empty. Seriously? WTF game?
Then his weapons fire and once again, both hit. The missile hits my engines this time, so that's fun.
My Burst Laser fires, and this time, I get miss, miss and more miss.
Please, game, let this be the one where I actually hurt him?
It's drawn out enough that he actually gets 2 volleys before my next shot. His first round of fire results in his missile damaging my shield room again, but I'm not too worried because I still have a layer of shields and the first set of damage has almost been repaired by now. I'm starting to regret trusting a Mantis to repair the shields though. The next missile hits my O2 again, destroying the room. And I've been keeping it powered down for more of the fight than I've had it operational. I'm down to 60% oxygen already. I rush my Engi down from the weapons room to fix this, because it's kind of important right now. Once my shields are back to 2 layers, I drop my Mantis in to help out.
My return fire is, once again, 2 hits and a miss.
It's not until my next Artillery Beam fires that I actually damage the enemy's shield room, which drops them to 1 shield layer, and from that point, the fight goes smoothly. Best part? When I finally hit the engine room, it only took one laser hit to destroy the engines. They did all that with only ONE power to their engines.
But wow, was it hell getting to that point.
FINAL NOTE: The

smiley indicates the point where I actually yelled at my laptop. Thinking back on that fight now, I can laugh. At the time, if someone else had laughed, I'd have been sorely tempted to punch them in the face.