Being a Tokusatsu show, there were tons, such as Tyranno Ranger wearing Dragon Ranger's armor, wielding his Dragon Strike Sword and his deceased brother's Beast Flute Dagger to obliterate Dora Anteus's heart.
The final battle between Geki and Burai, with the Tyrannosaurus Guardian Beast fighting Dragon Caesar in the background.
Right after Burai reforms and joins the Zyurangers, everybody henshins. If that wasn't enough, it's revealed that Dragon Caesar can be combined with Zyu Mammoth, Triceratops and Saber Tiger to form Gouryuzin.
Dora Sphinx gave Geki one question... "What's the most constant thing in this world?". Geki answers 'Justice', the correct answer according to Dora Sphinx is 'Evil'. But rather than being thrown to a tree immediately like the rest of the Zyurangers, Geki instead delivers a Shut Up, Hannibal! and is able to continue the fight until... other complications (necessary ones) was presented by Daizyujin.
And the next episode, the Zyurangers team up to answer Dora Sphinx's riddles until Geki challenged him to give question about his weakness. They purposely got it wrong, Dora Sphinx reveals his weakness and the Zyurangers kick his ass before Daizyujin can get thrown off to a tree.
Maybe it's not Burai, but in any time Mei gets a focus episode, expect her to do a lot of awesome:
Bandora even had to put her to sleep via poisoned apple so the rest of the Zyurangers cannot beat her current Monster of the Week Dora Ladoon. Instead of waiting for some cure, Mei instead got up with her own willpower and desire to help her friends (including taking a free leap to a sea of fire). Then she returned to battle and proceeded to wipe the floor with Dora Ladoon.
Against Dora Boogaranan... Mei, just fresh after being cured from being turned into a punk, just witnessed both Geki and Dan being consumed by said monster and she... ran off to a nearby woods. The monster gave chase and there came Mei, attempting to surrender. When the monster is about to eat her, it turns out that Mei already set up a bunch of traps in the whole wood just so she can shoot the monster's mouth (stuck due to the trap) and free the other Zyurangers... and she does that without morphing.
And against Dora Guzzler, a monster so tough that not even Burai and Dragon Caesar can beat. She just lied down there, ready to get eaten like her ancestor to destroy the monster, but before she gets eaten, she instead proceeds to beat the crap out of him until he's dead, and she's not in some monster's stomach. (Majorly unmorphed too, until Pteranodon gave a hand) Yes, you heard it right, when Burai can't beat one certain monster, Mei can.
Even if she had to get bailed out in the end, her transformation-battle against Lamie also count.
Episode 32. Geki is reluctant to fight the Dora Narcissus monster, as it has life-restoring properties that might save the life of Burai. During the fight, an armored warrior shows up and attacks Geki (while also keeping Dora Narcissus from doing so) and challenges his commitment to his mission and his allies, saying he only wants to be comfortable for himself. After Geki reaffirms his commitment to defeating Bandora and saving Burai himself, he defeats the warrior... and it turns out that the warrior was Goushi all along, fighting Geki to show him what's really important. It really shows how Goushi's title of Warrior of Wisdom fits him.
Episode 30 is one for Bandora summoning Dai-Satan. How? Summoning Dai-Satan is a risky spell that any mishaps would instantly kill Bandora. Her subordinates have been begging her to just stop anyway... Bandora will have none of that, she's finishing the spell no matter what! And... it works, resulting a series of two disturbing episodes that nearly brought down the Zyurangers. Yeah, she may be the Big Bad and eventually those plans fail in the end, but you gotta admit, this hag is persistent in an awesome-villain style.
Episode 44 was Goushi's, where he took down the Monster of the Weekin one blow, after having his shoulder cut open. Then he leads the team in calling Dai Zyu Jin and takes the helm in the following battle, coming up with tactics to beat the monster a second time. He doesn't get as much love as other second-in-commands, but that guy is Made of Win.