This quest is extremely annoying and requires a lot of tries and errors, since you have to shoot at the target from the closed position and you don't see where your shots land.
Here is a quick way to complete it. You have to get the ammunition and parts for the cannon from the Tranan Underfoe for 20 Energy first. Then click on the cannon parts in your inventory to see the location at the Cron Castle, where you should place the cannon (marked with the yellow light beam).

Go there, place the cannon on the spot and use the rotation, angle and max power (hold the LMB button, until the gauge fills to 100 as shown on the screenshot at the Screenshots tab.

The credit goes to the author of this video, which saved us all: https://www.youtube.com/watch?v=TE3iNpQ_0XE