The opening to Cruel Sea is probably the most memorable moment of the entire series, when Branagh narrates "The predator is laying in wait for its prey, waiting to strike," with a Eustreptospondylus peering into the ocean expectantly - when suddenly a giant Liopleurodon leaps out of the water, snatching the large theropod off the land for a tasty meal. The episode title card, "Cruel Sea", punctuates the moment.
Nigel Marven tagging the giant shark Megalodon in Sea Monsters.
The mother Dimetrodon defending her nest from the rival female in Walking with Monsters.
Another example from the same program: the tiny predator Euparkeria becoming a gigantic Allosaurus and frightening the croc-like chasmatosaur which chased it just before (like saying: "Yeah, sucka! Who's an apex predator NOW?!")
In a lot of media, ground sloths are portrayed as slow-moving animals that easily fall prey to predators. Not this one.
The fatal wound the sloth gives a sabre-toothed cat almost resembles a Dope Slap.
That awesome scene towards the end of the episode "Next of Kin", where our ancestors sent the Dinofelis running with its tail between its legs… by throwing rocks at it. No test of strength or speed; they used their brains and refused to back down.
The music. Just... the music, for all of them.
It ended badly, but you can't deny that the old male Ornithocheirus' journey in "Giant of the Skies" was pretty awesome; he's 40-years-old (which is bound to be ancient in pterosaur years), and yet he flew halfway across the world just because his sex drive was too much for him to ignore. And he beat death multiple times while doing it, given that he could have ended up getting eaten by a sea monster or mauled by raptors. Instead, he dies because the journey tired him out. Which, in a weird sort of way, makes it a Dying Moment of Awesome too.
Patchi saving Scowler (the dinosaur who picked on him everyday, kicked him out of the herd, and refused to call him his brother) from the Gorgosaurus. In fact, he and the herd work together to drive the predators back, and he even breaks Gorgon's arm with the hole in his frill and knock some teeth out. And the line he says shows how far he's come.
Patchi: That was for my brother, that was for my dad, and THIS (headbutts Gorgon, knocking out some of his teeth in the process) that's so how you'll remember me!
Don't forget the fight between Patchi and Scowler. Of course Patchi lost, but it's still amazing how he refuses to back down from his bullying brother.
Alex gets one when he snaps Patchi out of his Heroic BSOD by telling him that he should live or die for something worth living for.
Alex: Patchi, listen to me. Do not die in vain. If you want to die, die for something your father did. He died for you.
Patchi leading the herd safely around the frozen lake.
Gorgon snatching the Azhdarchid pterosaur out of the air.
And later, his winning fight with Scowler, which results in the biggest Moment Of Awesome mentioned above.