After completing the Medallion puzzle in Resident Evil 2 you will gain access to the Underground Facility area. This will also be your first encounter with William Birkin. Birkin is the scientist who created the G-virus who has also injected himself with it which has caused him to start to mutate.
Your first encounter with Birkin will be the easiest of the game as he’s not quite that strong yet. Though the process to beating Birkin at this point in the game is roughly the same as it is for the rest of Resident Evil 2. Part of the mutation for Birkin has eyeballs growing on his body.
In this fight there is one eye ball in particular on his right shoulder that is already quite prominent. To beat Birkin in this first encounter you will want to target this eyeball that is on his shoulder by shooting him with any guns that you have.
If you happen to run into this encounter with no low supplies of health and ammo there are numerous spots in this area where you can pick up more to help you out. You can check out the video below for a visual look at how to beat Birkin in the first Resident Evil 2 boss fight.