Actually, since I've had this problem too, I'd like to share my 5c on the question asked by OP:
- other forms of damage prevention doesn't count as long as the shots still miss, since evasion is proc'ing before almost everything else (shields/Zoltan Shields/resistance etc) except Defense Drones (and possibly other drones if you're [un]lucky), which block the shots preventing the evasion at all!
- your piloting/engines bonuses actually help you with getting this one, since you don't automatically get 100% evasion with cloak, but only +60%; it's imperative to get at least 40% base evasion before cloak to maximize the chance of getting this cheevo.
- the achievement is 100% gettable ATM, I don't know what was the case with it 2 years ago, but now you can 100% get it, and it's not bugged - but see below
- you actually can and should get it on wave 3 of Rebel Flagship - only bear in mind that it takes some time and luck to get it
- remember that misses before full shield activation doesn't count here and misses after the activation basically won't happen (since cloak stops weapon fire, it could only happen with asteroids) - that's the obvious reason why you rather won't be able to get it on every single try (and why you - and me too! - didn't get it on the first try)
The best way to get it is to actually:
- approach Rebel Flagship 3 (easy difficulty with AE disabled comes to mind if you're not an FTL vet),
- permanently disable Triple Leto Missile Launcher, since it's the only weapon capable of punching through the shields and posing a real risk for cheevo grinding (preferably by using a boarding party but fire bombs or concentrated laser fire works wonders here too), but leave the Heavy Triple Burst Laser intact - and remember to leave at least 1 crew member alive (AI!),
- remember that Hull Repair Drone, high base evasion and 4 shields are helpful on every difficulty above easy, but you can manage getting easy cheevo with just an almost-full HP ship and 3 shields with a bit of luck; mitigating the risk of Mind Control on AE is important too, but you should probably try getting this achievement with AE disabled anyway,
- wait for the Power Surge, as soon as you see the Flagship shooting the surge but before they enter your ship view activate evasion,
- rinse, repeat until Cheevo Get. This will happen most probably when the burst is timed with regular Heavy Triple Burst Laser shot.
The only thing that made me wonder is the fact that Power Surge actually uses 8 shots - I can't recall, but if every of them is 1 damage only, you actually have to have the surge timed with regular 3x Flagship Laser to be able to evade 9 damage. Alternatively, the description could be simply wrong in that it requires 9 shots evaded, not 9 damage (although I seriously doubt that); that would be the reason it's a bit harder to get this cheevo than to simply wait for RF 3 Power Surge.
Alternatively, you can get the asteroid field with some late-game enemy (as pointed out by Paul Marshall), although I'd say it's actually the harder way, since a) asteroid fields ain't that common in the endgame, b) there's only a slight chance you'll be able to encounter a ship with so high damage output in one burst, other than the mentioned Rebel Flagship
more info (although it's been mostly already stated here): http://ftl.wikia.com/wiki/Phase_Shift