To kick a man when he is down.

"kicking someone when they are down" may be the correct translation, but isn't really about false bravery. It conveys a sense of cruelty.

Michael, perhaps the first option you gave has the same sense of false bravery, but there is an exact equivalent for it in Spanish "perro ladrador, poco mordedor" (it means that a dog who barks, doesn't bite) and it doesn't really mean the same as the one I mentioned above ("a moro muerto, gran lanzada" means that someone attacks, and if I'm right "He's all bark and no bite" means that someone threatens but doesn't attack). The other ones, I've looked for their definitions and equivalents on the Internet and I'm not sure if they mean more or less what I need. I think that the most similar option is "To kick a man when he is down", although it doesn't express the idea of bravery in itself... Thank you very much for your proposals:)

Hmm. "He's all bark and no bite" seems too soft. "Paper tiger" seems to carry the idea, but not the sense of motion. An inversion of "talk softly, and carry a big stick" is tempting, but quickly risks going rude - "He talks loud ly, and carries a little stick" isn't quite there. "He's all mouth and no trousers", maybe . ..

what Yusuf said is the English proverb you are looking for.