I found that perhaps the simplest way to unlock this is to use the starting character Viktor.
ability is a grenade. If both you and your enemy are weak enough, you can toss out your grenade as they kill you. If it kills them, you will unlock both this achievement and:
This is because 0 health is, technically, still less than 50. The developers may change this since it may have been intended for you to still be alive when unlocking "Not Like This" but perhaps not as this is technically still correct. As of 3/14/2017 this works.
I will add other options as I find them, or feel free to leave a comment and I will credit you.
However, this is likely the easiest method.
Another useful method for both achievements is to play as Skye, run into a large group (especially near the objective), and use her ultimate which deals massive damage. You'll die and most likely unlock both achievements.
Credit for this method goes to Slayers Reign
Note that you must play against bots until your account level is 5 upon starting the game before playing against other players to unlock achievements. This usually takes 4-6 games depending on if you win and how well you play.