Claire attempting to raid Umbrella HQ BY HERSELF even though she gets caught, outrunning a helicopter that's shooting at her and managing to wipe out a whole crowd of Umbrella security guards in the process.
Claire's fight with the Tyrant. "Oh, nothing. Just a big cockroach that needed to be stepped on."
In The Darkside Chronicles, the rematch with the T-078 Tyrant is the same as before but the ending is a Moment of Awesome for the Tyrant. Claire and Steve throw the box of explosives at the Tyrant like before, but he actually catches it and throws it out of the plane! Then, they have the idea of shooting a missile at it. They shoot the lock off, and the Tyrant actually catches the missile and briefly holds it back!
Even Alexia Ashford gets her own Moment of Awesome in the original version when she takes on Albert Wesker. After all the crap he put you through in RE1, it is truly an awesome sight to see Wesker get his ass handed to him. What is awesome about Alexia is that she was a 12 year old girl who succeeded where a gigantic evil megacorp with countless devoted mad scientiests struggled. The ultimate goal for Umbrella was to turn a selected few into transhuman beings, borderline physical gods, and Alexia managed to do exactly that without seemingly losing her mental faculties and memories.
It's hard as hell to actually pull off that many fans believed it was just a rumor, but it is indeed possible to finish off Nosferatu using the knife, which Claire sinks up to the hilt in its exposed heart. And it is GLORIOUS.
To a slightly less awesome degree, you can also do the same to Nosferatu by shooting him in the heart enough times with the Sniper Rifle. Claire: "I've got you now!"
When you finally kill Alexia with the Linear Launcher, you are treated to a positively epic slo-mo shot of Alexia exploding from multiple angles.