If you follow Billionaire's Boss guide (look for it in this forum), you can get up to 13 hits for free on each boss. If you are under level 25, the top boss has 110,000 hit points, so you need to be at almost 8500 attack by the time you get to the last boss without gold.
If you are using gold, you can pay for the extra hits, and get there before your attack is that high.