on a slightly more serious note... if you have the AI programmed so that it never backs out of a fight... you're options are pretty limited! every version of the Nieuport is faster and climbs better. the Airco turns better, but is only marginally faster.
if you're flying in campaign missions I honestly think you should have "AI Never Backs Down" turned off.
with that in mind:
fly it the same way you would a Fokker Eindecker. the Halberstadt is only marginally faster and more maneuverable... so you should approach flying it the same way.
you have to be VERY selective about what fights you get into. in fact, don't even get into a fight until you've already planned your attack, how you want to disengage, follow-up attack, and escape path. (disengaging from the target isn't the same as your escape plan. it might be something as simple as how you plan to avoid getting killed by the observer's machine gun after a gunnery pass so that you can move back into a kill position)
the only difference in tactics (from an Eindecker) might be that since it uses an inline engine you might be more selective about how you approach turning battles. you can't 'cheat' your way through by using the inherent torque of a rotary engine in the same way. since most of your adversaries WILL be using rotary engines you'll want to plan accordingly: if you must turn, always try to turn in a way that puts those rotary engine machines at a disadvantage. (typically this means turning left)
you also need to manage your energy extremely well. don't give away altitude unless you can trade it for moving into a kill position.
generally it's better to wait for them (fighters) to turn first and then turn against them in the opposite direction. since the enemy planes are typically faster and can turn better - you need to reduce your time of being a target as much as possible. if you limit their attacks to nose-to-nose engagements while turning a lot of the AI pilots will not be good enough at shooting to seriously damage you under these conditions.
don't follow an enemy into a turn. they'll always out turn you. the key is to combine vertical and horizontal moves with good energy management. if they turn one direction, pitch your nose back, gain a bit of altitude, and then swing the nose down when you see them start to level out. then you can put yourself on their tail. you might consider turning against them so that you're flying over and past them into their 6 o'clock. now they have to gain altitude and turn back just to get into an attack position again.
also, if you find yourself in a defensive spiral, you may have to reverse your direction with a wingover if you sense the enemy is going to start overtaking you. you can't out turn them... but you can force them to take longer to get on your tail.
you should favor using the High Yo-Yo for attacks against fighters. this way you can gain a bit of altitude, lose a bit of speed, which you can then convert into both speed and increased turning power when you put your nose back down on target. hopefully, at the end, you'll wind up above your enemy by the time that maneuver is done. it works well against the Airco DH2 since both planes have comparable speed.
if you've got friendlies close by you might consider using a low yo-yo to increase your speed to cut inside of an enemy for a kill shot near the top of the zoom climb at the end of the move. but that's only if you feel confident in the amount of time you'll have on target and your marksmanship skill.
don't be afraid to waste a little bit of ammo if the situation calls for it.. it sounds crazy, but if you open fire at longer ranges and the bullets land close you can get an enemy in an otherwise superior aircraft to panic and close the gap between your machine and theirs. I did this with an Albatros DVa (200) the other night while I was flying a SPAD VII. if that Albatros pilot had kept his cool he would have just flown off and there would have been nothing I could have done to stop him. but since he freaked out and turned off to one side I was able to get close enough to seriously damage him.
I dunno... hope that helps.