Whenever you damage an enemy enough, they start glowing/flashing a color. When they do this, get in close and press 'F' to perform a Glory kill. Repeat 200 times for the achievement.
Additional Info on Glory Kills:
-The most important thing to note is glory kills will make the enemies drop health, ammo, and after a specific upgrade, armor shards. There are upgrades throughout the game that increase drops namely, Hell runes
-By default, the option to highlight 'staggered' enemies is turned on. This can be turned off in the settings for a more 'classic' doom experience.
-Looking at different areas on the body will sometimes do different animations. Experiment if you are getting bored.
-"Glory Kills" is an option in the "tutorial" section in your tab menu.
-Unless you're really trying not to, this should unlock before level 5
-Some challenges require specific glory kills.
They all count toward this total.
- There are Hell Runes and suit upgrades that make performing glory kills a little easier by increasing stagger time or the distance at which you can initiate the kill.