Aliens Colonial Marines

Basically fight as if it was a real fight left/right hand jab, step back, right/left jab, step back. Don't rush in let him come to you mostly.
i had to uninstall the games update. That big alien just wouldn't ever die and the little aliens were killing all my shields and 1/3 of my health each time. ( usually just getting into the loader, I lost half my health) After removable of the update it became easy to (left or right) jab & step back, ( use the other hand) jab & step back, repeat til he lowers head to rush you may be able to get a jab in but be careful (he is quick) regardless you'll get caught). If you manage to get him cornered on a wall give him quick alternating left/right jabs. He'll grab him with the claw after a few to choke alien ( you'll get hit with acid). Repeat the alternating hand jab & step back technique.
My first play through was on the level below badass so i had to choke him three or four time before he stayed down. But soon as he's beat the level/mission is over and you get the achievement. ( I didn't get the timed achievement cause took me a while to find the technique, I got from a youtube video but don't recall the link)

Solo Solution

This isn't an easy task on Ultimate Badass difficulty but hopefully I can give you a few suggestions to make things a lot easier for ya.

-As soon as the mission begins you will behind the iconic loader suit. I recommend taking out the first two smaller "Lurkers" right off the bat before entering the suit.

-Your first priority has to be the Lurkers as they will drain your energy in seconds if left unattended. The best way to deal with them is target them in your view (you will not have the HUD in Ultimate Badass) and click the RS when they are in medium to close range, it seems to be very effective against them killing them in one shot, instead of the suit's punching animation which is slower.

-When attacking the boss try to keep him off to your right side so that he is barely on screen. Punch him with RT. Try your best to pin him in, the corner underneath the slight overhang where the suit was initially is a great place to pin and corner him allowing the AI clear range to take out the smaller Lurkers.

-Contrary to popular belief YOU CAN PICK UP THE HEALTH PACK WHILE IN THE SUIT! It is located on the crates across from where you get into the Loading Suit. Picking it up during this fight is almost a must!

-There will be THREE automatic animations in which you choke the boss with the Loading Suit claw. I found if you picked up the health pack after the first one you are in good shape. After the three there is a fourth animation in which you will twist him in half and the fight will end even if you have Lurkers remaining.

Don't be ashamed if this takes you multiple tries. The controls are sketchy and a search will reveal a multitude of others encountering the same problems with this tough boss.