Пробить means to break through, hit (not necessarily punch) through. In spoken, informal language, the word can mean to achieve a hard task that required overcoming difficulties. I can only guess the origin of a slang usage. Most likely, it comes from the military where breaking through an enemy's armor or bunker is a difficult, often necessary task. With most Russian men having served in the army and in the case of the older generation fought in a war, the language is rich with expressions originating from military terms. You can probably figure out what object Russian men call pilotka. 
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