The hard difficulty Whack-a-Box challenge opens up in Chapter 14 in Sector 5 Slums. The aim is to get a score 30,000 points within the time limit to complete all 3 challenges. Destroying boxes gets you the score indicated on the box and destroying red clock boxes extends the timer. You'll want to prioritise the time extenders as you progress.
When tackling the larger boxes or a large group of boxes, switch to punisher mode. Once you're done, roll in the direction you want to go as this will break you out of punisher mode while keeping you moving. Do not try to move around in punisher mode as you'll waste huge amounts of time.
There are three main sections blocked off by large boxes. The exit to first area is blocked off by two of them, and you'll want to get up to at least 7,000 score by the time you tackle them. The exit to the next section is blocked off by one, and I aimed for 19,000 at this point. Make sure you get the two large boxes with the time extender behind it before leaving. Then work your way through the third section to the time extender right at the top and work your way back if you're still short on points.
Below is a video of me completing this using the method above. In this run I've not used any special abilities and I'm using the Buster Sword.