Retrostage: I spend ~15-20h playing FTL and stil have problems to beat the game on easy. I've beaten the first encounter with the rebel ship, but the second, I'm always lost. Now, I reached the last secotr and I'm in a better position with better weapons (you need a lot of luck to find good ones that are helpful), cloak, teleporter and max weapons/shields. I hope that this time I can beat the game but I must say: It's REALLY hard, yet challenging. It's fun to play, but my only real chance is to master the game with the Kestrel (+ B layout).
I have also the Engi Cruiser, the Stealth Cruiser and the Mantis Cruiser, but only with the Kestrel, I'm able to reach the last sector.
I think, I read enough guides and saw enough youtube-playthroughs, but I can't imagine beating the game on normal mode.
Perhaps I need a litle bit more luck, we'll see...
I haven't unlocked any of Kestrel achievments. My best score and gameplays come from Engi cruiser.