To do something valiantly is to do it bravely and with valor. Heroes are known for doing things valiantly. Firefighters save lives by valiantly running into burning buildings.
To be valiant is to have courage and to persevere, especially in difficult circumstances. Therefore, to act valiantly is to show courage and perseverance. A basketball player with a sore ankle who helps win the game has played valiantly. A war hero served his country valiantly. Martin Luther King worked for civil rights valiantly. This word has to do with strength of character and fortitude. Acting valiantly is difficult, which is why others admire it.