Nami is partly justified because she lacks the insane superhuman strength and/or Devil Fruit powers a lot of her crewmates have, so she must rely on her brain, wits, and Clima-Tact to survive in battle. As she gets skilled with the Clima Tact (and is upgraded to the Perfect Clima-Tact and later the Sorcery Clima-Tact), she becomes more courageous. Even when she's pushed against the wall, she's not afraid to use lethal levels of heat, cold, or lightning on her opponents. But she'll only do that if she feels like there's no other option, and frequently comments about how she's in over her head.
Chopper is fairly young, shy, and sheepish. He freaks out a lot and gets shook up in bad situations. Post time-skip, he's more in control. He also frequently wants to prove his manhood, so if there's some sort of situation where he can prove that a bad guy doesn't know what he's in for, Chopper will take it, pushing aside doubts about his power to do it.
Usopp's a funny case; as long as everything is fine, he's a total Miles Gloriosus. But the instant there's the slightest hint of danger, and particularly when he's the only one who can do anything about it, he upgrades to Cowardly Lion. When any significant danger presents itself, Usopp will panic, then proceed to kick ass despite shaking in his boots the whole time. As Sogeking, he tries to ham it up under the facade of a capable badass, but the disguise melts away as soon as real danger comes his way or he gets annoyed. After the time-skip, he gets a bit better, and resembles a real badass, though with some cowardly traits still very much intact. It just takes a much higher level of threat to bring them out now.
Karoo from the Baroque Works Saga is a lesser example.
Shinji Ikari in Neon Genesis Evangelion. Normally a timid, withdrawn, and slightly neurotic person, he gets surprisingly confident when he pilots the Evangelion, but he quickly falls back to his usual behavior outside of it.
Mr Satan in Dragon Ball. And to a lesser extent Krillin.
Zig-zagged, especially during the Saiyan Saga, where he's just as likely to panic and cower in a corner at a crucial moment as rise to the occasion. His level of bravery seems directly proportional to how hard the villain is hitting his Berserk Button.
Jacuzzi Splot from Baccano!. The guy knocked over eighteen Mafia-owned speakeasies in one night by himself, with a single Tommy gun, crying hysterically in fear all the way. The week after, he helped save a train from two clashing terrorist groups; to do this, he did battle unarmed but for a single cherry bomb against someone with a shiv knife, a fist-gun and a flamethrower (which did turn out to be pretty convenient for lighting said bomb) on top of a moving train. He took a couple of bullets in the gut and a knife in the elbow before he tackled the other guy off the train and won. He was later half-carried to the station by his girlfriend, moaning in pain.
Sir Penwood is the prime example in Hellsing. Part of the Round Table, he is well-aware that he is a nervous man not suited for battle and war and knows the only reason he got his position was through inheritance, yet he stands by to do his duty all the way to the bitter end, where he blew himself and his base up, taking a massive amount of Nazi vampires with him and inspiring his subordinates to stand by him during London's invasion. It's little wonder why Integra and the other Round Table members have great respect for him as well.
Seras Victoria herself is this. Serving as an Audience Surrogate for entering the mad world of being a vamprie, she was initially a normal police girl, though with a troubled past. As she overcomes her truamas, she outgrows this to become a full Badass.
Kobanzame of the Kyoshin Poseidons is another example. A nervous nellie of a quarterback, Kobanzame thinks he's useless and leaves all the major decisions to Kakei. Yet he has perfect ball handling, and on short passes is a perfectly competent player. Reiji Marco, captain and quarterback/safety of the Hakushuu Dinosaurs is a villainous example—he's utterly terrified of getting hurt, yet continues to use himself as his own best piece, risking his neck to lead his team to victory.
Simon from Tengen Toppa Gurren Lagann is like this initially. Scared of all the things happening around him that nearly kill him, but if Kamina is in danger he opens up a can of badass at a moment's notice.
Kamina is also a Cowardly Lion, but puts on the face of a Fearless Fool in order to keep Simon inspired. He admits as much to Yoko, while also saying that if it weren't for Simon's brains, he'd have bitten the dust ages ago.
Closer from Hyde and Closer. Always run from battle, Hyde always had to bail out his ass, but never let his friends in danger, even if that means takes the beating all for himself.
Kamiya Maki of All Rounder Meguru first finds Aya huddled in the corner of a room at a kickboxing event. She darts off like a rabbit the moment Maki tries to talk to her, leaving Maki bemused to discover that Aya is actually her next opponent, and astonished to find that she's the most formidable opponent she's ever faced in a kickboxing match.
Asura from Soul Eater could be a Deconstruction of one. Born with fear in his soul, his fear of the outside world and possibility drove him to fight alongside Shinigami-sama and other warriors to make the world a better place. However, these fears overwhelmed him, turning on his comrades and becoming a horrible monster and threat to humanity. Especially since as a Great Old One and Shinigami's offspring (as in Kid's older brother), he possesses the Madness of Fear, his presnece driving people into insanity through fear. To Asura, fear is a motivator, but in the sense he wants to drive everyone insane and or destory all in his path to quelm his fear.
A more example is in Crona, Medusa's "child." Despite that fact that zhe is constantly afraid of pretty much...everything, zhe will not hesitate to take on bigger scarier enemies if it means helping hir friends. Given how zhe was made by Medusa to try and recreate the Kishin, this makes hir a foil to Asura. Especially in the manga, where Crona ends up back as a Heel and absorbs Asura before Maka knocks sense back into hir and Crona becomes a Barrier Maiden to seal off Asura.
At one point, Kenichi is induced with a 'mental seed of fear' after a near-death defeat by one of his enemies. It took the efforts of one of his teachers who essentially invoked this trope when she did not intend to not cure him of his fear, but rather to teach him to weaponize it as a means of self defense in order to overcome its negative effects.
Kain Fuery in Fullmetal Alchemist. He's the smallest and youngest member of Roy Mustang's hand-chosen unit, and his main value is as the communications specialist. When the team gets split up and he's reassigned to the southern war front, he's absolutely terrified and only gets through it by shouting at himself that he's going to live. Later, he deserts in order to return to Central City and aid Mustang and Hawkeye with their coup.
And then we have Warrant Officer Falman, who was literally crying and shaking with fear as he defied Bradley's order to open the gate to Central palace. Captain Buccaneer called him on it.
Buccaneer: Oh come on now. Don't cry like a girl when you act like a man!
In Demon Slayer: Kimetsu no Yaiba, that's the actual core of Zenitsus character; on the surface he is cowardly, is always complaining about something, screaming at the top of his lungs that he should just run away and give up on being a demon slayer, turns out that despite of all his incessant tantrums Zenitsu never actually runs from the heat of battle, to the point he just developed a kind of trance sleep mode where he can bravely fight against his foes while being somewhat unconscious thus unable to fear what is in front of him, and as the series progresses Zenitsu becomes able to fight more as himself instead of always relying on his trance mode.
Kai Shiden of Mobile Suit Gundam with emphasis on "Lion". An abrasive jerk who perpetually points out the stupidity of the situations they're in and often seems about to panic when sent into combat, Kai's nevertheless a reliable solider who racks up a pretty impressive kill count over the course of the war. He might have easily ended up as one of the Earth Federation's most celebrated aces, if not for being the wingman of the White DevilAmuro Ray.
While Ranma Saotome of Ranma ½ is a Combat Pragmatist, he's generally pretty far away from anything that resembles cowardice... unless cats are involved, in which case a few seconds after being surprised by a housecat he is literally catatonic and will eventually lose his mind from the sheer terror until he starts thinking that he's a cat and starts kicking the ass of almost everything within eyeshot using the ultimate technique, the Neko-ken. However, when he was tossed into a situation that almost perfectly replicated his initial trauma (being tossed into a pit of hungry cats while wrapped in fish products), he managed to (sorta) maintain his composure until they brought out a tiger that was about as tall as he was, at which point he snapped. Later on, when facing a grandmaster that was casually kicking his ass and holding his manhood hostage, Ranma deliberately strapped a cat onto himself (or rather, herself) in order to pull out the Neko-ken and get his opponent to back down. That is to say, he deliberately drove himself insane with fear in order to win a fight.
Kasumi of King of Thorn. She believes she is weak and useless, having depended on her braver twin sister Shizuku for most of her life. Later she depends on Marco for protection and often needs him to rescue her. However, she's still able to put her fears aside long enough to save someone else's life. She even saves Marco a few times, and earns his respect for it.
Arata Hinohara from Arata: The Legend is understandably scared to fight and follow his destiny in the beginning of the series, but he follows through with completing the task at hand, anyway. As the story progresses, he gradually grows out of it.
Suigetsu from Naruto tried to run away from Team Taka as soon as he gets the chance, despite being made of water and completely impenetrable. Too bad non-combative Karin is faster than him and prevents him from getting away.
Attack on Titan has many of these, which is understandable considering what they are upagainst. Among the main characters, the following stand out.
Sasha Blouse is a Cloud Cuckoo Lander, and breaks down during her first battle. She even apologizes to a Titan she'd failed to kill, and agonizes over it later. But she's also managed to charge down a 50m wall to rescue an injured comrade, and faced down a Titan with nothing but a hatchet and a bow to save a child.
Bertolt Hoover readily admits to being an Extreme Doormat, and constantly stands there awkwardly with a slightly terrified expression. He's also ranked 3rd in their class, and is noted by their instructor to be one of the best at physical combat. He's also the Colossal Titan that smashed open Wall Maria and Wall Rose.
Any soldier that shows fear prior to combat. It's not uncommon to see the same person that was weeping hysterically prior to battle turn into a Hot-Blooded warrior when the chips are down. Unfortunately, since it's that kind of story, many of them still die horribly.
Yugi Mutou from Yu-Gi-Oh!, who is timid and sensitive, conflict-averse, would rather turn the other cheek than escalate the situation whenever someone is a jerk to him, and believes himself to be weak and cowardly, despite showing astounding courage and grit from his very first appearance (standing up to a bully twice his size to protect Jounouchi and Honda, who had been mercilessly bullying him prior to that moment) and growing progressively more confident over time, finally truly realizing his own strength at the end of the series.
In Fate/Zero, Rider praises Waver Velvet for being willing to ride with him into battle despite being scared out of his mind.
Izuku Midoriya from My Hero Academia. As he goes to rescue Ochaco Uraraka at the beginning of the series, he is lying on the ground, shaking and crying in fear, but upon seeing her in danger he knows immediately what he has to do. This is also the reason he receives One For All; not because he is immune to fear, but because he does the right thing DESPITE his fear. Even as his control over his new power grows, he never quite shakes off his nervousness and fear of dangerous Villains, but it never stops him from rushing in to help others need.