Use your dodge
Resident Evil 3 is a much more action-oriented title than its predecessor, and Jill is equipped with a dodge roll to encourage you to get up close and personal with the undead inhabitants of Raccoon City. Nemesis is incredibly fast, and just running in the opposite direction will only get you so far. He'll sprint and jump around in an attempt to stop you from escaping, and once he's close enough, he'll unleash a devastating attack. Just because you're close to Nemesis doesn't mean you have to take the hit. Plan your dodges well and you can avoid taking damage. This is also useful when Nemesis bursts an arsenal of different weapons during the game. It's a great skill to master early on.
Don't worry about ammo
As we mentioned above, Resident Evil 3 is much more action-oriented than Resident Evil 2, and ammo is therefore less scarce as a result. While Leon and Claire had to count every last ball, Jill and Carlos have a little more leeway with their arsenal. If Nemesis is giving you a hard time and you can't seem to get past him in one spot, then don't be afraid to take a few punches at him and force him to stop and recover. After taking enough damage, Nemesis will take a break, just giving you time to walk past him and head to a safer area. Even though it takes the majority of your ammo, there are always more bullets around the corner in Resident Evil 3.
Hang in there and get a free item
If you manage to deal enough damage to Nemesis, every now and then he'll leave you with a free item to take. In the early game areas, forcing Nemesis to give up an item can earn you a free weapon attachment, while in other areas you can earn bonus supplies. You'll also earn a trophy or achievement the first time you do this to him. If you have a grenade on you, use it instead of wasting ammo unnecessarily. Also keep an eye out for generators or explosive barrels to deal massive damage to Nemesis when he gets close to them.
The environment is a weapon
Even if you don't have a lot of ammo on you right now, you can still deal massive damage to Nemesis if you use the environment to your advantage. Red explosive barrels are much more common in Raccoon City than you might think, and a well-placed shot can deal a heavy blow to Nemesis if he's nearby. Plus, there are generators everywhere that can cause fatal shock to anything nearby when knocked down. Shoot them when Nemesis is about to briefly stun him and give yourself a chance to get out of it. The same goes for large crowds of zombies. Always be on the lookout for environmental hazards as they can help you get out of a sticky situation if you use them.
Don't be afraid to run
There is no shame in that. He is stronger, faster and more resilient than you. Sometimes it's better to just cut and run. Of course, you can get some sweet items if you can manage to deal enough damage to it, but it might not be worth fighting if you run out of supplies. Even though it's more action-driven than Resident Evil 2, Resident Evil 3 is still a survival horror game at the end of the day, and running out of supplies comes with the territory. Jill can absolutely stand up to Nemesis if you have health and ammo reserves, but if you're injured with no healing herbs in sight or barely have enough bullets to make it to the next safe room, you probably should. do your best to evade enemies until you are better equipped. Find a safe place, grab what you can from the item box, and save your game. Then come back there and see what you can do.