You HAVE to get into a close range (5-8" range) furball with the Klingons. He will have a much harder time keeping his front shields away from everyone if you get in close and swarm him. Although it is counter-intuitive to do so, if you have a closer Klingon facing you, and another in arc facing away at some other ship, take the shot that's longer but hits the flank. It takes some discipline to shoot at the Klingon who is shooting your buddy instead of shooting the guy in your face shooting YOU, but you score more damage faster if you hit the other Klingon in the flank.
Fight as if you don't have Photons and you intend to win with with your Phaser-1s. If you get a decent Photon shot, take it, but don't get fixated into chasing a more maneuverable target trying to get that perfect shot. Not likely to happen unless you get lucky.
Split into groups but stay within support range of neighboring groups, say 9-12" or so.
If you can't get your target in the Fore arc so you can hit it with Photons, at least try to get the target into a position that maximizes how many Phaser-1s you can shoot at him. For a Fed CA, try exactly at the 3 or 9'oclock positions - this allows your FH, RH or LH, AND AH phasers to bear and if you can keep out of 4" Phaser-2 killzone it allows you to outgun most Klingons. Don't forget the aft centerline - most people forget you can get 6 Phaser-1s firing directly aft as well.
If you have awful ADD rolls like I do, try using your drones against incoming drones - you kill them 1 for 1. While it isn't theoretically as efficient as using ADDs, you can't run out of ammo this way. Obviously this works better if you choose some drone-heavy ships (Fed escort, BCH, DWD) and keep them on Intensify Defensive Fire.
If you have to shoot at Klingons in the front shield, at the least take advantage of the rounding rules and split fire between mounts. If you have say 2 banks of 2 dice Phaser-1s, don't fire a bank of 2 at one target, fire 1 die from that weapon system at 2 different targets. Then repeat with the next mount. If you fire both dice from one weapon system at one target that has it's front shield pointed at you, even if you hit with both, you lose half the damage. If you split fire between 2 targets, one halved and rounded up is still one hit times two targets. Effectively double the damage, even if is spread out between 2 targets, each one takes as much damage as one would have it you had fired both weapon systems at one target. Goofy rule, but use it to your advantage.
Related to above: if his shields are getting low, and you are shooting into his front arc, fire one weapon system at a time, taking the half damage penalty until his shields drop. Then any subsequent weapon systems fired are at full effect. If you had just lumped all your weapons into one big batch of dice you lose the opportunity to do more damage.
The Klingons are definitely beatable, once you learn the right tactics. I used to think they were unbeatable as well.
