The Call of Warr: Glintz-Terry is horribly afraid of the trees, and gets easily flustered and scared when dealing with a stressful or upsetting situation- but he's also a dedicated soldier who will stand by the others, even if he doesn't want to.
Cobra Kai: In the second season, this would become Demetri's defining trait. He joined up with Miyagi-do because he didn't want to be perceived as a pussy. While it took him forever and a year, he stuck solidly with his training, and (faced with an Outside-Context Problem where he tried to get a teacher's help) it paid off in no small way during the school brawl when he disposed of Hawk with one good kick.
Happy Tree Friends: Flaky has her moments. Unfortunately, this doesn't always save her or anyone else.
Kurt acts like a very nervous and cowardly contestant in Mindcrack Ultra Hardcore and prefers not to fight when he can, but when push comes to shove he shows a terrifying martial ability, as proved by his takedown of Pause in Season 3, his leading the charge against Team Veterans in Season 4a and dropping Nebris from 10 hearts to 2 before Nebris even touches him in Season 7.
RWBY: Blake Belladonna is a highly skilled warrior who can function in battle along side adult Huntsmen and who wants to become a Huntress to fight against hate; however, Blake believes she was born a coward who flees her problems because her Semblance creates decoys that take the hits for her. She fled the White Fang when it became too violent for her, she fled her team when they learned she was a Faunus, and she flees Vale when Adam threatens her friends' lives. However, when she finally stands her ground against Adam in Volume 5, it isn't until her final confrontation with Adam at the end of Volume 6 before she can put this belief to bed, after Yang reassures her that she believes Blake's promise to never run again.
Whateley Universe: Phase. While Team Kimba fearlessly charges into fights against supervillains, Phase is the only one who's really frightened. He still dives in like everyone else. He has claustrophobia, and his best trick is walking into solid matter which sets his phobia off. Or maybe he's the Only Sane Man in a comic book world.
