Location challenge. Four explosive charges are needed to fill the sockets on the asteroid.
One can be easily found on the station, but it is attached. To get it off, shoot a breakable panel below it to reveal a red button. Shooting the button will release the charge.
The second is also at the station, but is hidden behind another breakable wall - keep an eye out for a blinking light. Alongside this charge is one of two power cores.
The third is below the station, inside a small opening.
The last charge is behind a metal wall and pipes built into an asteroid below the rigged asteroid. This one is harder to get to and requires powering up a mining laser to destroy a hardened ore patch blocking the way to get the charge. The laser needs two power cores - one that is found near the second explosive charge, and one that is found near the fourth charge and the wall. Plug the cores into the laser and after a few moments the ore patch will be destroyed (dropping clymouth) revealing an entrance to get the last charge.
Once all charges are inserted into their sockets on the rigged asteroid, they need to be activated within a 10 second time period (refreshed each activation) to blow up the asteroid, which then drops Clygon and Clygon Cores and completes the challenge.