The Nemesis lives up to its name in Resident Evil 3, following you and the general kicking you. You will eventually get used to the perpetual shadow that appears and hits you with something, but you might be curious to kill it.
The quick answer is, no, you can't, but you absolutely have to fight him anyway at certain points in the game. There are two very specific points where it makes sense to fight the Nemesis and spend a lot of your money. ammunition to drop it for a short time.
If you manage to force the Big Man to kneel at certain points in the game, he will drop a Supply Box with upgrades for your handgun.
The substation
The first time you need to properly engage with the Nemesis is when it comes to you outside the substation. You have to get him down here, and he'll drop you a crate of supplies. You can catch it quickly and then run away from the monster.
It's not a bad place to fight him, as you can use nearby barrels to do extra damage, then pump as many bullets as you can into the center of his chest. Once you've finally gotten away from him, check the case and you'll get an extended magazine for your handgun.
After the train puzzle
The second time you want to take him to Nemesis is after doing the train puzzle. As you make your way to the subway, make your way to Moon's Donuts and you'll find the Nemesis giving a zombie a tentacle-based makeover. It's much easier to drop him here, as you can hit the electric generator next to him, forcing him to take a knee. This time, he'll drop a holster containing the handgun moderator.
These are the only two times Nemesis will drop something this way, and if you miss them, you won't be able to get them back. So while you can't kill Nemesis, you should definitely hurt him on both of these occasions.
