To press an attack relentlessly — to assault continuously, whether militarily or by persistent verbal/critical attack.
敵の陣地を夜通し攻め立てた。
They assailed the enemy position throughout the night.
記者たちは大臣を責任を追及し、質問を攻め立てた。
Reporters pressed the minister relentlessly with questions about responsibility.
彼らは相手チームに休む間もなく攻め立てた。
They attacked the opposing team without giving them a moment's rest.