I give the same advice to anybody asking for general help, and it applies here. See below for that.
One thing about the Osprey, though, that beam is TERRIBLE at level 1. At level 2 it's pretty meh and at level 3 it's okay. But at level 4 it's AMAZING. Granted, it's expensive to get it there but it should be a priority whenever you have spare scrap instead of buying anything that could be considered a luxury.
Also, I consider the teleporter a detriment to this ship. Either you want that beam tearing the ship apart, OR you want to be teleporting over. If you're playing the Osprey why ignore its biggest asset to play a toned-down version of the Kestrel? With no cloak and no teleporter to worry about, that beam should be easy to level up and power.
Here is my personal checklist of things to do. I try to follow it with most every ship:
Before the end of sector 1, 2 shields (4 bars)
Before the end of sector 2, 4 engines.
Before the end of sector 3, 3 shields (6 bars)
Before the end of sector 4, 5 engines.
Also, you need to have a way to get through:
Before the end of Sector 2: 2 shields (Most ships can do this)
Before the end of Sector 4: 3 shields (This usually means you need to buy weapons or a teleporter in sector 3)
Before the end of Sector 7: 4 shields (or the Boss is gonna suck)
Note: to get through 2 shields, you need to do 3 laser shots. Or have 2 ions and a laser/beam/whatever. Or have a teleporter. Or a bomb. Doesn't matter what.
THEN I start thinking about upgrading other things, like doors and O2 and medbay and stuff.
Most of the time I don't reach these milestones, and I end up not getting my 4th engine until midway through sector 3 or something. No biggie, as long as you keep trying.
Never, ever, ever, EVER buy missiles. Unless you simply must because you've not found a way to get rid of your missile weapon. They are the single biggest resource drain in the game if you buy a lot. The next big resource drain is repairs. Any time you show up at a store needing a ton of repairs, that's a weapon you can't buy, or drone control or a cloak or long range scanners or who knows what else.
Ions are great in groups, but not so great by themselves. 2 Ions will eventually take down ANY shield so long as your opponent doesn't dodge too many of them. An Ion and an Ion 2 will reliably take down ANY shield eventually. Once those are down, you can use your other weapons to actually damage the ship.
Try to get 2 of these 3 things before you meet the flagship: Teleporter, Cloak, Defense Drones. A cloak and a level 5 engine will make you unhittable while the cloak is on, and you'll be dodging 1/3 to 1/2 of all shots fired when it's off. Add in a defense drone and you're essentially safe from most everything but the occasional lucky shot (and bombs, but those generally aren't a big deal as most can't damage hull). 2 mantises and a teleporter are your friend, make it a priority early so by the time you get to the later sectors your mantises are fully leveled up, and they will be killing machines.
If I may humbly suggest, I've beaten the game on camera with every ship in the game (and a few mods) on Normal and while I get into (and out of) some sticky situations, for the most part I walk over the bad guys because I stick to what I've said above.
Check out my thread here.