I've managed to reach the point where get through the entire thing on a regular basis, so I'll throw out some general tips(lots of text incoming):
- Get shields level 4 asap, or at least fairly fast. You take less damage from stuff, and you're going to want that upgrade for later anyways. That being said, don't completely down-prioritize weapons either, as you do need to kill stuff. It's a matter of balance.
- Get a full crew. Should be self-explanatory, but just do it anyways. Also, having several races on your boat can be a massive help, because they can fill different roles. It doesn't matter as much what roles you take, but for the love of god, don't get a pure mantis or pure engi ship. You'll die horribly. Humans, slugs and to some extent rock(or crystal, durr) are the most well-rounded races, mantis are great as boarding crew, engi can repair shit and not much else, and zoltan are just really nice to have. Still, maxing out the crew and getting them leveled is more important than the crew composition.
- Make sure that your weapon layout can take out shields without resorting to missiles. This means that for earlier enemies, you can save missiles for tougher ones, and it means you're not screwed at the final boss(phase 2 has a defense drone). Obviously this isn't always doable at any part of the game, but you should still aim for it.
It also means you won't be screwed if you run out of missiles.
- Shoot shields first, ask weapons later oh god that was horrible please kill me for even thinking that
..sorry. Anyways. Your usual tactic for most ships will be to disable their shields so that you can reliably do damage, then take out their weapons. If they have high evasion, fire a barrage at their engines or their cockpit(the first one can often be knocked out in one hit, reducing evasion to 0% temporarily) and then continue with the above plan.
- If you have multiple laser weapons, fire in volleys. Kind of obvious when you think about it: just fire all your weapons at roughly the same time to make sure the shields get taken out and the maximum amount of shots penetrate. If you have heavy/hull lasers, fire them slightly after the other ones so that they're not wasted on the shields.
This is very important if you want to effectively use beam weappons. Take the shield down with a laser volley, then fire the beam. Try to have the shield room as the first target for the beam, and then drag it over as many rooms as possible to maximize damage. If you have a halberd beam or a glaive beam, this tactic can destroy a ship in a single volley.
- Grind out sectors. You want to get to the exit beacon one turn before the rebels, if possible. The reason is simple: you want as much scrap as possible, as well as the possibility to get more crew other random stuff. Also, you might get a new ship, if you're lucky.
- Get a teleporter, if for no other reason than to destroy the missile launcher on the boss. That thing is beyond any doubt the most dangerous thing on that ship, superweapons included.
Beyond that, boarding ships is great fun. Another thing to note is that if there's no mantis and no upgraded blast doors on the enemy ship, you don't need to upgrade the teleporter. If your boarders take too much damage during the engagement, just run from room to room on the enemy ship until the teleporter has recharged.
- Learn to use doors properly. They're one of the best pieces of equipment on your ship. You can use them to put out fires and weaken/kill boarders, without putting your crew to risk.
- Don't upgrade stuff immediately after combat. Check if there's a shop in the neighboring sector first, you might want to buy something there rather than spending a lot of scrap on an engine upgrade.
- Early scrap recovery arms are great. If you get it by the first 3 sectors, your total income will be ridiculously boosted and your ship will be so much better late game. They're not worth the cost late game, however, as you need 500 scrap collected for the arm to pay for itself.
- Stay out of nebula sectors unless you have a long-range scanner. Ion storms are the worst hazard to face by far, and nebula sectors don't give the same chase bonus that other nebulas do. If you have a scanner, however, nebula sectors are fairly nice. There's still a small chase bonus(I think), and the scanner gives several blue options in the nebula.
- Stay out of rebel sectors. There's just no reason to go there, apart from killing rebel scum. Few good events and rarely interesting crew members. Also, if a rebel scout gets away(and there are lots of rebel scouts in rebel sectors), you lose so much free time in the sector. Blergh.
- Ion weapons 101: If they're not paired with another ion, they suck. Don't even bother, just get another laser instead. The notable exception is Ion Blast II, which can perma-disable shields.
If they're paired with another ion, they can be good, as you can perma-disable shields.
If paired with an ion blast II, they're flat-out overpowered. Fire the IB2 at a system you want taken out, and the other ion at the shields. Both of these systems will be permanently disabled, because the initial IB2-stacks on the shields will stay up thanks to the other ion weapon, and the IB2 will take care of the other system.
As you might have guessed from that last paragraph, my personal favorite ship is the regular engi ship. If you can get a second ion weapon and a drone recovery arm, you won't even have to do anything to win: just select two systems you particularly don't like, have the ions autofire at them, and proceed to fire up your drones(I'd suggest using anti-ship I, beam I and defense I as drones. Effective and easy to get). Pump the rest of your scrap into defensive upgrades, and make sure to get non-engi crew and blast doors to be completely safe from boarding parties(med-bot dispersal <3). Cloak kind of sucks with this setup unless I get stealth weapons, though, but that's not even relevant before the boss.
That being said, there are a lot of effective weapon-, system and augment combinations in the game, so don't hesitate with experimenting. And if all else fails, you can teleport your entire crew onto the enemy ship and bludgeon everybody to death like a man(I beat the final phase of the rebel flagship by doing that once, because I ran out of missiles. It was hilarious).
Hope that helped a bit. Good luck with killing the rebel scum and saving the galaxy!