I found this easiest with an X-PAC mortar alien weapon and by overcharging the suit. There are a couple of these mortar weapons and alien power source "crates" around the outer ring.
When the suit is overcharged, you can fire the mortar without depleting ammo, and it does devastating damage to this boss. You'll have to aim a little bit high in order to get the mortar rounds to connect, but playing on the "normal" difficulty I didn't have any trouble taking each of the arms down with 2-3 volleys. I didn't wait for any particular vulnerability, I just shot the mortars at the arms like mad.
Sometimes your suit will tell you that an attack is incoming - when it does, you want to get to the outer ring and hide. Although overcharging the suit supposedly makes you invulnerable, there are a couple of "insta kill" attacks it has that bypass this.
The boss really can't hit you that well if you're on the outer ring, and you're up against the inner ring wall. Just hide out for a couple of seconds while the attack passes.
Once you've destroyed an arm, the boss will pick you up and you have to mash a button to keep it from killing you. When it drops you, there will be enemies that spawn. Run to another alien power source and drop your mortar, then deal with the enemies. Once the boss returns, overcharge the suit, grab the mortar, and repeat the process.
There are sentry guns hanging around that can help you take down the lower level enemies the boss spawns, if you want to hack them between rounds of arm destruction. Just make sure you stash your mortar weapon first, so you don't lose it or have to drag it to the next alien power source when the boss is active - it's heavy and slows down your movement speed.
There are a bunch of other bits of stuff hanging around here, so you can use the disposable rocket launchers or hit it with arrows if you so choose, but I found the mortar to be the most direct and easy to employ solution.