The Bullseye badge is for "Headshoting 50 enemies"
A "headshot" is just hitting an enemy in the head with any throwable. I recommend using bricks as they can be picked back up and used a second time. What counts as hitting the head is also very lenient so don't worry about being too accurate.
Also two handy things to note:
1. The in-game badge menu tracks your progress.
2. Leaving a trial after gaining progress still counts towards it.
Video guide for reference: