I'm playing the Commando, Axton, in Borderlands 2, and I'm building my character with heavy emphasis on the turret by using my skill points on upgrading the turret's damage, duration, and cooldown time. However, I'm not exactly sure how to upgrade turret damage outside of that. So what factors (other than level) effect the damage that Axton's Turret deals?
Beyond skill points and level, I'm aware of no other factors that directly affect Axton's Turret damage (ignoring things like Slag, which are properties of the entity being attacked, not of Axton or his turret).
It's worth noting that the Dahl Engineer class mod provides Sentry skill points, which will increase the turret's DPS (though not the damage per hit).
I recommend getting the missile volley which definitely increases damage. Get a slag sniper rifle to make enemies more vulnerable to non slag damage. A class mod to keep the turret out longer and you're set.
Throw your turret out, take cover safely far away, and shoot enemies that your turret is currently targeting with your slag weapon. Your rifle will coat enemies with purple slag and your turret will destroy them in seconds.
I've taken down those higher level gigantic plant/tentacle like creatures that live in the sand in a 4 player server by myself with this strategy!
Aside from player level there is nothing that increases the actual turret damage per shot. The best way to increase the firepower that thing's throwing out is to increase Sentry (increases the amount of rounds the turret fires per burst), laser sight (the amount of rounds actually hitting the target), Scorched Earth (which adds an occasional rocket volley for excellent added damage) and Double up (deliver's twice the number of rounds as before and slag effect, which combines with Scorched Earth's explosive damage works wonders).