If you keep dying quickly, try ignoring defense. Build an offensive monster and overwhelm Typhon (and friends) with massive firepower. Load as many big bad weapons as you can. Spend some time maxing your Speed and Initiative before the fight, so you can launch everything you have faster than the enemy can get more than one or two shots off. For weapons, try nukes, single-shot high-DC long-range monsters (if you have Sniper), and/or missiles with a high ammo count and mid-to-high DC (the heaviest ones come with very few missiles, so ignore those). I recommend Superheavy Particle Cannons for the sniping since they're very long range and fairly strong (IIRC range 108, DC 13). You might also try Heavy Gauss Rifles (IIRC range 96, DC 24). Any special effects that improve damage (e.g. Armor-Piercing, or Brutal to tear down external armor) are a plus. Since I think Typhon flies, Anti-Air will help. I'm pretty sure all Particle Cannons have AA btw.
Note that missiles are probably your best bet for a purely offensive mecha. They use Sensors instead of Targeting. I think they also use Perception instead of Reflexes, though.
If you use guns instead of missiles, aim for the weakest limb. You'll focus the damage on one spot rather than spreading it over his 6-10 body parts. The overkill damage when you destroy a limb can destroy the torso if you hit hard enough. If your skills aren't high enough to reliably hit limbs, aim for the torso instead, since no torso = dead.
If your all-out offense fails, bring friends. Lots of friends. Can't find friends? Build 'em! Robotics is pretty sweet in GH1 (and doesn't exactly suck in GH2, though it's a Talent rather than a Skill). Let them rush into battle ahead of you to draw fire. High Leadership will net you extra lancemate slots, I believe.
If all-out offense with friends fails, I guess you need to spend more time leveling. Maybe add a high-end ECM suite and boost Electronic Warfare for extra defense.
I'm pretty much out of ideas at this point. Just remember that what JH said: You only need to kill Typhon. Ignore his allies. Don't worry about trying to survive the fight. Just kill that son of a bitch any way you can.
Oh, wait! One last idea: Shields. Lots of shields. Give yourself several extra arms with shields and melee weapons. Every shield and melee weapon should give you an extra defense roll AFAIK. Beam shields/weapons are preferred, since they take no damage from ballistic/missile attacks.
Also, I think mounted (hand or mounting point) weapons have a slightly better attack bonus than installed weapons. Get some mounting points. And arms may have a bonus over other module types. And while I'm at it, I'll recommend weapons with a high ACC rating over special effects if you're trying to kill with raw damage. In fact, I'm pretty sure Haywire and several other effects won't work on Typhon since it's BioTech instead of Metal. I never tried, myself, since I usually focus on damage over effects anyway. Then again, I'm not a particularly good player either. I do have a fair bit of patience for grinding, though, and that helps.