My advice for people trying to complete under 3 hours....memorizing where you need to go, and the fastest way to get there is key. I played through the game as Chris first, and my gametime was laughable because I hadn't played RE in so long, but once I was familiar with the layout of the mansion, my playthrough attempts as Jill were cake because I knew where everything was. Don't do what I did and attempt to beat under 3 hours and do your no save run though, that was what made me pull my hair out a few times, because of instant death traps like the rolling boulder, and Lisa pushing me off the edge.
Another thing though is knowing when to fight and when not to fight. If you know you're going through an area that you won't revisit often, do not worry about killing a zombie. If one's in your way, if you think there's an opening to get around it without attacking it, take it....if you absolutely must attack it to make it past, just do it enough to where it falls down, but don't worry about killing it. In some areas though you may want to kill some of the zombies, and burn their bodies if you think you'll be going through the areas frequently enough where it's faster to get rid of them than it is to avoid them.
I was able to spare time for weapons and ammo in my under 3 hour run on normal, and having the right gear can also help you shave time off your run. Getting the magnum and saving it for the end boss can be really useful I think, and make it go super quick. Also if you're strictly going for the under 3 hours, don't worry if you heal yourself often. If you get attacked by a zombie by just getting past it, and need to heal, just do it.