Episode 6 of the OVA should be mentioned for two things: The introduction of Washu, who destroys two giant snakes who were trying to eat Mihoshi, who inadvertantly freed her, rescues Ayeka from being killed by Kagato, and stands up to Ryoko, while revealing that she's her mom by creation being one. The other being Tenchi's return when he saved Ryoko by chopping off Kagato's hand, plus when he activates the Light-Hawk-Wings for the first time and defeats Kagato in a classic duel sword strike that cuts BOTH Kagato and the ship Soja in half!
Washu is in full badass mode during her whole confrontation with Dr. Clay in the "Zero Ryoko" episode, but it gets even better when, after Dr. Clay has trapped her in some kind of jelly-like material, she breaks free, punches him in the face, and then(even though he dodges it) throws a big-ass chair at him! Dr. Clay abandons ship after that. I would too.
And believe it or not — Mihoshi gets one of these, which is followed by Kiyone getting hers. She and Kiyone are fighting Tsugaru, so Kiyone gives Mihoshi a very dangerous anti-matter weapon and then poses as a decoy, hoping to distract Tsugaru enough to have Mihoshi shoot him. Tsugaru then attack Kiyone at full strength... and Mihoshi, instead of sacrificing Kiyone, shields her with her own body and collapses, seriously wounded. This gives Kiyone the Heroic Resolve needed to take the anti.-matter weapon and blast Tsugaru into oblivion.
Tenchi in the first movie, Tenchi Muyo In Love, "I won't let you touch my mom!"
Also in the first movie, Achika shows off a bit of badass-ery confronting Kain in the Tokyo Tower. However, she ramps it up into Took A Level In Bad Ass after being sucked into the alternate dimension. When she finds out Kain beat the living hell out of Noboyuki, Achika snaps and taps into her latent Juraian power the same one that would kill her years later, telling Kain just one thing:
Achika: I have had enough! I will not allow this! I will pay you back!(Transforms) Because forgiveness... for one like you... could never be an option.
Nagi from the Tenchi Universe. She may have only been around for one season, but she was a total Bad Ass bounty hunter.
Sasami whipping out a staff and kicking Mishisu's butt was one of the high points of the Third OVA.
Ayeka's reaction after having learned Sasami's story in the OVA. "We love each other. That's what counts."
From the first episode of Universe, Katsuhito totaling a mecha with one hit using just a wooden katana.
Pretty much the entirety of the final OVA episode. Z managing to utterly own both Tenchi and Lady Tokimi, Washu and Tsunami performing a Big Damn Heroes to put Tokimi in her place, Ryoko doing whatever it takes to save Tenchi, Tenchi manifesting as a god more powerful than the goddesses AND saving Misaki from her counter-actor state...
Katsuhito is shown holding his own in battle against Kagato in the fifth Tenchi Muyo OVA, even when Kagato had a mind-controlled Ryoko get in on the action. Even got in a cheap attack on the space pirate when he duped him into grabbing Tenchi-ken and feeling its nasty effects.