Stumbled upon an ancient gamefaqs thread on the matter:
https://gamefaqs.gamespot.com/boards/431704-resident-evil-3-nemesis/52759515

Dodging and a bit more.

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[Page 16] - Some Basic Keyboard Actions
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Key(s) - Action
Space, Enter, C - Select/Action/map (Zoom In/Out)
Esc, V - Cancel/Run
B - Change Target
S - Draw Weapon (towards enemies only)
X - Draw Weapon (towards all targetable objects)
Z - Toggle Status Screen
M - Display Map, Press M again to view map list.

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[Page 21] - Advanced Actions
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DODGE
Press the 'Draw Weapon' key (Keyboard X/joypad R) the moment an enemy attacks you.
Note: You cannot dodge when you are severely injured.
Attack... Press the Select/Action key (Keyboard Space, Enter or C/joypad A) while holding down Keyboard X/joypad R)

Dodge attacks
Draw Weapon... Hold down Keyboard X/Game Pad R
When an enemy grabs your character or your character is down, you can escape more quickly by rapidly pressing the directional keys and a button such as the Select/Action button (Keyboard Space, Enter, or C/joypad A), Cancel key (Keyboard Esc or V/joypad B), Draw Weapon key (Keyboard X or S/joypad R), or Change Target key (Keyboard B/Game Pad L).

Quickly press the keys repeatedly.

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[Page 22] Advanced Actions continued.
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- QUICK 180 DEGREES TURN
Press the Cancel button (Keyboard Esc or V/ joypad B) while moving backwards (and pressing the directional Down Arrow key) to turn 180 degrees.
- ATTACK OBJECTS
In some areas of the game, certain objects can be used to attack enemies by shooting at the objects. These objects are called Attack objects.
When drawing a weapon towards all targetable objects with the Keyboard S key, you will be able to search for targets according to their order of priority. This can prove to be very useful against enemies.



To clarify all that mess, there are two ways to dodge. One is to press X (and possibly S) as the enemy attacks. Those are the keys for readying the current weapon. It's been reported that weapons that take longer to ready give a larger window for dodging.

The other way to dodge is to attack with a readied weapon. Pressing (or holding) spacebar while holding X or S. This can interact with the keyboard repeat of holding down the spacebar. Dodging is almost guaranteed to work due to the key auto-repeat.

- When mobbed Jill can end up continuously dodging, until she's in inescapable trouble. That's the downside.

- If all goes well Jill will dodge or fire as appropriate. That's the upside.
-- Using this technique with the Magnum can squash Nemesis like a bug.

"Spacebar auto-repeat, eh? That's actually quite cunning...

That may well mean that the advice I'm about to give isn't such a great idea.

I was going to say that I found the game a lot easier to play using a USB control pad, which is basically the same as a playstation controller. But that might make it harder to dodge while aiming if this is true about the spacebar.

I think it's true that dodging works better when you're using a weapon that's slower to draw. I found that the best bit of dodging I ever managed was when I was surrounded by about 5 zombie dogs, and I had a shotgun. I had it drawn and I was mashing the fire button AND draw weapon button. They couldn't touch me. It was awesome to watch.

What I never could master was how to do the dodge-roll-low crouch-shoot maneauver with a pistol. Apparantly it lets you fire really fast for a bit after a dodge, but I could never ever do it.

By the way, this PC version of the game...

Is it or is it not the "Xplosiv" release? I hope it's not. That's what I got, and wished I hadn't. Just thought I'd mention this just in case...

You see, that particular version has the Mercenaries mode removed, and you cannot save your game after you complete the game once, so you can never ever get any special unlockable weapons. It's truly awful."

It's also interesting that the key to beating Nemesis seems to be frantic keybashing. Either mashing the Fire key to dodge, or the arrow/other-control-keys to escape.