The normal difficulty Whack-a-Box challenges open up in Chapter 8 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.
When you start quickly head to the right to get a time extender. Break through the first large box and head over the bridge and make sure you get the time extender behind the large box to the left. Progress through the two large boxes and there's another time extender here. Then break through the next two large boxes and switch to punisher mode to destroy the pyramid, making sure you get the time extender at the top. Head left and break a further two large boxes as there's another time extender behind that. If you still need more points work your way back the way you came cleaning up the groups of boxes you've not destroyed yet.
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.