Things I've learned about surviving mecha combat with objective complete and mech intact (mostly from Gearhead 1, at least partially updated to Gearhead 2):
Things you really have to watch out for hardware-wise are, "BLAST," "LINE," possibly, "SCATTER," really high BV/range guns and targetcomps. If you still do get hit occasionally but shrug it off from armor then you also have to be really paranoid about, "OVERLOAD," and, "HAYWIRE." I suggest you steal one of those .5 ton 1-slot computers from a Trailblazer loaded with a mecha catalogue and an awareness +3 SW if you haven't yet, this'll let you know what you have to be scared of and help you see it before it sees you. If you're really good at gunnery/artillery yourself consider cutting fights short by hitting the enemy in exposed ammo launchers that haven't run out of ammo to make them go boom, double-bonus if it is ammo with a, "BLAST" flag and you aren't within range. (Favourite trick to get rid of chimenteros and anything with those bazookas.)
If you can find four spare slots for it also the 1t/200ZeG computers on Luna IIs (1 quarter the weight of the same capacity of computer from a parts shop) can hold a +2/+2 TR/MV software set--the part you need most for improving longevity is probably the MV bonus so you may prefer +1/+3 TR/MV software distribution instead (or even +2 Speedcomp/+3MV or just +3MV and the software from the Trailblazer's computer if you want to save a slot and .5t). This will increase the PV a lot and any missions that scale by PV will jump in difficulty dramatically (bigger mechs with more, bigger guns).
If you can get it you may also increase your defensive mileage with a certain piece of software I've salvaged in my arena games that takes 70ZeG and gives a +2 bonus to piloting skill without affecting MV, the lightest computer you can install this in comes from Vadels (and maybe some other mechs) which is a 0.5t 100ZeG computer (2 slots).
If your MPs are low you may do better to stick the 30 ZeG mecha catalogue/analyzer whateversoftware in the same 100+ZeG computer as that +2 piloting software (70 ZeG) and give up on the +3 awareness--this depends on if using awareness software inside a mech spends your MPs like using a data visor does on personal scale. This is to avoid the tired penalty to all actions from exhausting your MPs.
As always keeping your mecha moving at high speed by boosting its movement powers is probably your best general added protection, especially if your stealth isn't much higher than their awareness. Currently you can see if it is and how much it is so by looking at the rolls history (R). If you forego stealth moving at top speed the stunt driving talent can come into play, allowing you to reroll your mecha piloting which is generally the most powerful defence roll you get against attacks. Acrobatics also may help if you're good at it (and holding a pair of ribbons?) if your mech's supplemental armor is no higher than class 2, and an ECM gives you an additional defence roll using electronic warfare against most things--exercise this skill regularly with lots of OVERLOAD, BURN, HAYWIRE, RUST, and other special-inflicting weapons, overload especially because once you've hit with it this will make whatever you hit with it both easier to hit in future and less capable of hitting you with things that aren't artillery. Note: With the innovation feat, that set of lightened class-1 armor you get from a Trailblazer can fit an arcjet 6 in each piece, or maybe, if you're really lucky, a few of the super-light heavy actuator 5s from an ovaknight if you do most of your fighting on land and actually think you can risk some melee combat.
To improve your MV/TR ratios you are best off mounting your weapons on mounting points, this halves their effective weight for penalizing MV/TR. At the same time weight absolutely lowers speed and even halved weight still penalizes MV/TR: A non-augmented battroid mech with a standard 7 mounting points (1 head, 1x2 arms, 1x2 legs and 2 for torso) costs 3.5 tons by itself for the mountings which can make a difference particularly with smaller mecha.
As far as tactical behaviour goes: NEVER SIT STILL, this is the quickest way to die. Make sure to use available cover to improve your stealth and try to end your turns behind tall mountains where you can't be seen if you can (and are using turn-based combat). I love arcjets because they let you fly high to see enemies without their cover and also hover to make use of some yourself while still moving at a good speed.
In GH1 it used to be that to turn the quickest you possibly could you should switch to walking mode, turn and then return to movement in whatever mode fits your tactical agenda because otherwise it takes longer while you're sitting still and can't fire (with hover mode) or takes a really long time and sent you swinging in a huge arc in which you couldn't fire (in flight mode). I don't know exactly how much this is so still but using the default settings for squad based tactics (I've got action/time bars for everybody in my unit and then it's the enemy's turn), I find that you should set your movement type to whatever you want it to be when you're done turning because shifting modes almost always takes as much time again as turning does and you want to minimize time spent moving in a movement mode that's too slow or turning since that is strictly a period of vulnerability with no redeeming features tactically. Also, be aware that movement mode change seems to happen AFTER the movement itself with the very specific exception of letting you jump to flight mode to avoid skimming off a cliff. The progression <i>seems</i> to be turn/move/mode-change although I don't really know because I'm sick of looking at C code all day and can't be bothered to learn Pascal to hack source.
Things I miss from GearHead 1: The personal scale plasma cannons with a pair of barrel extenders. Those were awesome for hitting drones without wasting real weapons--even though they were too weak to kill them usually it often let you hit more than one at once like a tiny fly swatter. I also liked having ranged weapons that could reach my enemies a turn before they got close enough to shoot me, possibly forever if my jet was fast enough and I was shooting backwards with a turret. In arena mode the maps aren't big enough to try that trick even if I did have the range.

Note for balance maintainers (Mr Hewitt and whoever else helps him with these issues I guess): The system currently seems to let you design a SF:0 computer with 500 points of capacity (if there's no hidden barrier I'm unaware of), if you were to install that in a mech suddenly you'd have a 1 slot, possibly .5t computer more powerful than any other in the game. This aspect of mixing size factors for mecha engineering may need to be addressed. I'm also curious just how much SF:0 junk I can pile into my mech before it makes a difference in SF:2 weight... can I still pile up tons and tons of repair supplies and gizmos for robot construction (possibly army deployment) or have I been cut off from having a limitless vault I drive in? (I know it always increased the PV but if you've read the above guide you can probably guess that this never troubled me much except for XP gain lost.)