I decided to figure out the exact location where he stands and this is all you need to get this setup to work. Use Leon's left foot (it needs be slightly inside railing of the capsules) or the shadow of the character as a reference to see if you're in the right position.

The most important part about this fight is the starting position. This spot is consistent and fail safe due to Birkin having to turn towards you at a 90 degree angle. Quickshots can be performed here, but it's risky and can ruin the setup if you drop aim. In most cases Birkin will jump to the edge of the capsules.

Position for G3 phase: https://gyazo.com/6920020a48bfe16f42b0408e45a925e0 (Left) https://gyazo.com/3f5d7b54f1f0ee1337298694efd03464 (Right)

For the G4 phase of this fight, the whole purpose of this trick is to force Birkin into an AI loop since he's constantly trying to jump towards the player. I posted pictures below for a reference point on where you need to stand. It doesn't have to be the exact same in the pictures. Pay attention to Leon's left foot while aiming where the blue highlighted part is. It will be slightly inside of the railing where the capsules are and you can use that to dictate if you're in the right spot or have to adjust a bit. It'll take some time before you can pull this off quickly without thinking twice. I also use the lettering on the floor as another reference :p

The area highlighted in blue is where you want to pay attention for this. You don't have to be standing in this exact position, but make sure Leon left foot is some what visible through the railings on the capsules here when positioning. Once you're in position you can freely shoot Birkin without taking damage. The most shots you can fire before Birkin jumps is 3 (4 if you're quickshooting perfectly). It's impossible to hit him mid-jump from here. There's also a very rare chance that Birkin can grab you from above, but this only occurs if half his body is sticking out when he's above you.

Position for Jikka's G4 phase: http://imgur.com/a/zsZ6p

Demonstration

Quickshooting isn't necessary, but will result in a quicker fight.

It can also be done on the opposite side.