You'll come across your first Angels in the Mother boss fight. As you know if you've fought them before, Angels come in two parts: first, you see them as a stationary arm whose health bar must be destroyed. Then, they will spit out three Angel Cores, which look like exploding barrels. These only stay out for a few moments before the Angel sucks them back in; that's why you need "perfect timing" as the achievement name says.
The easiest way I've found is to destroy two that are close to one another by using a grenade (you must have unlocked it with skill points and equipped it with the radial menu, then you can use
) to drop it), then shoot the third if it's further away. If you don't get this right away, don't worry, you will see plenty of Angels, and you can replay missions.
Here is a clip if you'd like to see it visually: