Explore the lower laboratory area more closely and you will find an egg room (this is the room above the part where the scientists die and spawn nematodes). Approach the eggs to trigger a fight with the worm boss. Kill the worm boss (much easier with an SMG or magnum). Take the key that is in the room. You can then take this key to the leftside building foyer, then down the stairs and to the doors to the right of where you got your first handgun and fight the slime boss. You can kill the slime boss by climbing the ladder, running towards the red barrels to trigger the grabbing hand and then running left until the hand goes away. Once the hand attack is on Cooldown, go to the red barrels and rapidly tap Z to push them over the ledge. Then shoot the red barrel. Repeat three times until the boss exposes its red core. The boss will shoot the arena and make the upper floor more dangerous by covering it in fire. Keep shooting the red core (use the safe section of the upper floor for healing and safety) until it dies. I have no clue what the benefit of killing this boss is.
