The trick to beating the trigens, I found, is this:
1. Keep your weapons fully loaded at all times
2. Hope that when you see a trigen, they're at least 30 rounds away from you
3. Blast the crap out of them as they're running straight for you.
4. If there's 2 of them, a well-timed grenade throw will make your life a lot easier. You'll still probably run out of ammo on one gun and have to quickly switch to another to finish them both off though.
5. If there's 3 of them, the rocket launcher is a handy thing to have. Otherwise, try to find higher ground where you can pick them off one by one.
For the big mean rocket launcher trigens, just stay out of range of their melee attacks and dodge the rockets (their splash damage is pretty pitiful so this is easy), while hitting them with the heaviest weapons you have. Often near these guys you'll find a mounted machine gun or a vehicle with a mounted weapon that makes taking them out even easier.
For the last level in the volcano caldera where it's basically impossible to even carry enough ammo to kill everything,
an office chair pushed under the bunker door will stop it from closing and allow you to go back in and resupply whenever you need to