Doctor Zachary Smith from Lost in Space is a classic example. He regularly boasts of being able to "imitate the actions of a Tiger" if provoked and also of being able to fight his "weight in Tigers" too. However when faced with any actual danger he either cries, screams, faints or cowers behind an 8 year old boy.
Kevin Webster in Coronation Street often mentions how he's going beat up/flatten/decapitate people he's angry with, but he only has the bottle to pick fights with a teenage goth, and even then, said Goth sends Kevin running with his tail between his legs. He was also frightened of David Platt, when he went on his rampage, instead leaving it up to Ken Barlow to stop him. He's also terrified of what will happen if Tyrone finds out that Kevin's been having an affair with his wife. Kevin's father Bill is similar, with his boasting about how he'd swing for David Platt if he didn't have his grandmother Audrey to hide behind. Tyrone Dobbs recently told Bill that he sees where Kevin gets his cowardice from. While Kevin did wallop the crap out of John Stape after discovering Stape's affair with his daughter Rosie (and got a prison sentence for assault), John Stape is not exactly much of a fighter.
The Brigade Leader, the Brigadier)'s Mirror Universe Evil Twin, in the Third Doctor serial Inferno. Unlike the no-nonsense Deadpan Snarker Brigadier, the Brigade Leader is a rude and erratic Large Ham.
Pex, a Parody of '80's ActionHeroes from Paradise Towers, though he ultimately redeems himself.
Captain Cook from "The Greatest Show In The Galaxy" is a particularly boring, particularly cowardly and a particularly villainous and reprehensible version of this trope. Its a minor moment of awesome when the Doctor, even as he's at Cook's mercy with his life is on the line, finally has all he can take of Cook's waffling and tells him to shut up.
Finn Hudson from Glee, who talks a much better game than he plays when it comes to being a leader, and who tends to reinterpret his own ignoble actions in a much more heroic light in hindsight. His habit of claiming others' achievements (or a whole group's achievements) exclusively as his own - particularly in the matter of football game victories in which he was actually a minor player at best - puts him in this camp.
In an episode of Foyle's War, the Asshole Victim was a sailor who'd been given a medal and showered in praise for "rescuing" several of his comrades when their ship was sunk; it turned out that saving them had been purely incidental to saving himself, and that he'd actually shot one of them to keep him off a piece of wreckage he didn't think could hold them both.
In another episode, an old wounded WWI veteran who is considered a hero by the people in the area turns out to have shot himself in the leg to escape the trenches (and thus has a possible motive for the murder, since the victim was the only person who knew this). It's played with, however, in that rather than just being a coward and a braggart it's implied he was a victim of 'shell shock' who just couldn't handle the pressure of the trenches anymore, and he's portrayed as deeply uncomfortable and guilt-ridden about his reputation to the point of nursing suicidal tendencies.
The West Wing had a general who C.J. found out was planning, as his last act before retirement, to do a bunch of TV interviews claiming the U.S. was unprepared to defend itself with a wishy-washy liberal president in office. She shuts him up by threatening to point out in public that among his chestful of medals he wears (and has a phony explanation for) one he was never awarded. It's subverted, however, when Bartlet calls her in to tell her to back off; he might not have earned that particular medal, but he's got a lot of genuine ones which in Bartlet's eyes have earned him the right to express his views.
Farscape brings us Durka, one of the most legendary heroes in all of Peacekeeper history, who turns out to actually be a Dirty Coward who killed one of his own officers, faked his own death, and abandoned his crew to be slaughtered when a battle finally went against him. Unlike some examples, his cowardice doesn't stop him from being a serious threat if he gets the drop on someone or manages to persuade people to do what he tells them.
Neelix from Star Trek: Voyager more then qualifies. If he claims any skill rest assured that as the episode plays out he will slowly and deliberately prove that the opposite is actually the case until he's shown to be completely incompetent in whatever he claimed expertise in. Until his very last appearance on the show, where we're reminded that he's actually a Crouching Moron, Hidden Badass (we also have to remember that he not only survived reasonably well on his own in the Delta Quadrant, but also saved Kes and won her love). During his last appearance, he goes direct into Let's Get Dangerous mode when he fights to save a Talaxian colony, nearly has a Last Stand when he fights alone to save them, and chooses to stay to protect them.
Mac in It's Always Sunny in Philadelphia constantly claims to be a master of karate and have the skills of an eighties action hero. He's repeatedly shown to be a coward and gets beaten up in fights.
Reg Trotter from Only Fools and Horses. Del describes him as "a bit of a hard nut" with women and children, but not much bottle when it comes to other men.
Joffrey Baratheon Game of Thrones pretends to be a warrior prince, but actually got beaten up by a girl with a stick, and whenever actual danger nears he cowers. Perhaps best exemplified by his Monument Of Humiliation And Defeat, a statue of him killing the symbol of one of his enemies with his crossbow, while their defeat actually came about by an act of vicious treachery that he didn't even have anything to do with arranging, and happened while he was hundreds of miles away.