to push on; to plunge forward; to push one's way to
彼は困難があっても突き進んだ。
He pushed on even when there were difficulties.
風雨の中を突き進んで山頂を目指した。
We plunged forward through wind and rain toward the summit.
信じた道を突き進む覚悟がないと、途中で折れてしまう。
Without the resolve to push forward on the path you believe in, you'll break down along the way.