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Space Bombs work well though if you know how to use them.
Alien Fighters are easy if you keep your distance, there's just so many of them. Not to mention the Cruiser seems to keep spewing them no matter how many you destroy.
Another important thing to remember is that the Alien Cruiser only has shields, which can actually makes escorts like Corvettes with their dual las-turrets much more effective than you'd expect. While my experience was likely altered by the fact that I'd gotten lucky and stolen a Confed Cruiser for myself, I was able to waste it on my first try simply by siccing 4 corvettes and 2 Kestrels on it and trying like hell to stay close and pummel it with turrets. Just keep at it and remember your escorts lasers still work fine on that monstrosity.