This achievement is really a test of player skill and game knowledge. Knowing how and when to dodge, block, and whittle away at hordes and melee elites. I, admittedly, got this by accident, but knowing the layout of a particular mission, making sure not to corner yourself, and work with your team to stay healthy. As you must play the Veteran class, I recommend the Voice of command Blitz, because the gold toughness will really help with this. Picking up yellow stims to recharge it faster also helps, but if you're in a group with multiple veterans with VOC, than it should be a breeze.
If you're considering weapon choices, I would pick the recon lasgun, because it is the best at whittling away hordes of poxwalkers, with the Bolter and Plasma Gun next, as they can take multiple enemies with single shots. The last two do chew through ammo faster, though. I would pick a melee option with crowd control (shovel, power sword), but any will do if you prefer the moveset and playstyle. For grenades... well, Krak is the best one, because it can one shot Crushers at any difficulty, which is often the most difficult threat due to their armor and health.
For keystone, there is the select the target one, which makes elites you point out glow gold and take extra damage. This can be immensely helpful with Ragers and Maulers, the biggest threats to this achievement. Ragers for their fast movement and blur of attacks, and Maulers because they are tanky, yet not worth a grenade. If you do have the build, though, and go to either Damnation or Auric levels, well, taking the one that refreshes a grenade with every elite kill is not a bad choice. However, it is very likely you will take chip damage at some point, so Malice is the best choice of difficulty.
This does not include ranged damage, so if you get hit by a sniper or any type of gunner, it's not lost. Just keep calm, find cover, and eliminate the threat when there are no melee units near you. Just make sure to keep a 360 view when your toughness is below 100%, because all melee enemies can damage you even if you have your toughness if it's below 100%.
Really, it's up to the player to just get gud and win this. In terms of mission choice, though... avoid operations, and pick some of the earlier missions. Just avoid cultist only missions, as they include tons of ragers, which are the most likely enemy to have you fail this achievement. The first mission in the list, the chasm station assassination, is probably the best one because it is a Moebian only mission. Lots of gunners, but no ragers.