Follow the other guides for a rundown of how the battle goes.
I struggled with this battle on the lower difficulty and was getting ready for some frustration when it came to my Commando playthrough, but because of that I found a great way to get it done.
So, even on Commando difficulty, there is an easy way to finish this fight very quickly. You just need to prepare in the previous chapter (I know, with the 'save' system, that might annoy some people [sorry!]).
In the previous chapter, you will be releasing 3 cooling towers from the Constructor. While you are doing this, DO NOT use the Bulldog (grenade launcher). (Not too hard if you use the trick with the Mech's). Once the cooling towers are done, grab your fully loaded Bulldog before you head up to Groeder.
Start the fight as normal. you'll need to get 4-5 grapple hits in; white=jump, red=dodge. Once he starts pulsing with electricity, unleash on him with the Bulldog's grenades. He is invincible for a second or so after each hit - just wait until he stands up again (the same as you will have probably noticed with the Mech's throughout the game). As long as you get your timing right, he won't fight back. 4-5 shots and he's done!
Even on Commando difficulty, he'll die fast, before the flying drones even appear. Easy!