There's quite a few tricks but it depends on many factors..
One you could try flying fast forward, then slow down a little then slam the ship into full reverse. Use Kero/moonshine during the change in speed (tap Moonshine but use kero for longer.. ) This only works if you have more than half the engine health with all your engineers on engines briefly. You can attempt to do this without the speed boost. Factors to remember, you need to get above or below the ship, so start your altitude change before hand so that you can get above or below the ship. (Above is preferable, below is a bit easier to pull but more risky cause you be in arc for longer)
If you're very close to the edge of the map, run 90 degree to it and off the map. The game will "blow" you back onto the map, and give you a huge boost to changing speed, you could two things, either slam into reverse and do above or you can use claw to turn 90 degree again, and pull back and you get a nice sideway drift going and hopefully you be facing their side when they get blown back from the edge of the map.
If your balloon is full health and not disabled, you can try a tap of hydro and slam reverse on and go up then as you head up use Phoenix claw. (It's a little less damaging then kero but not by much.. use only if you have no engine disabled or about to be disabled.
Engines are disabled, then slam your throttle to full reverse and tell your engineers and gun to go into tank mode for the time. Help with hull or balloon depending on what ship you are on and have one engineer repair main engine first then one side engine (repairing side engine will make you turn.. I tend to forget which) OR if you want to attempt to turn and get some guns in arc, repair the two side engines first, when the ship start turning get back on the helm and speed the turn up with claw, maybe you can belt down some damage to disable their guns and get a few more time to have your allies help or just distract them longer so hopefully your ally can get one ship down and chase this one when you go down, 2 for 1 exchange. You can also try adjusting your altitude so that your ally can have a easier time getting to him.
That's a lot of the things you can do when you get into this situation but the best course of action is to prevent it in the first place. You're chasing a ship down, don't stare at the ship, let the gunners do that. Pilot tunnel vision is worse then gunner or engineers tunnel vision. Look around you, while it's not your job to spot ships, more eyes in the skies is better, if you see a enemy ship, you can use V - S - w/a/s/d/r/f (this is the signal for Enemy spotted Above/Port/Below/Starboard/Ahead/Astern) to alert your crew and hopefully whoever have time, to spot it for you.
Use the map, I don't hear many people do this but I've switched my keybinding around, so Tab is my map window, M is the player list. You can do whatever is comfortable. You can often tell when a ship has switched focus by looking at which way the arrow is pointing (you're the blinking one) If you're chasing a ship and it looks like the other one is about to chase you or is chasing you.. Full reverse then stop (slow the ship down and turn faster), use claw to turn 90 degree (to the port side on a pyra so you're turning to the gun side of the ship to them) then when the turn is done, kero backwards.. hopefully you're no longer showing your butt to a possible aggressive enemy by the time the one chasing you get into range.
Be aware of what is effective with your build. If you're a disable ship and it's look like you're about to get focused by the enemy team, disable one ship, get out of their arc quickly, disable another if you can get another in arc or get the hell out and run to your ally BEFORE you actually get focused. Always run away backward.. the only exception is galleon and junker and even then, it's better to run backwards then to expose your engines.
Finally, Always look around, check the map, think ahead, predict instead of reacting. (example, it's 3v3, you have two enemies ship engaged, don't see the third.. look around, it might be trying to flank you while the two are distracting.)
Good luck in the skies
