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

Quest has been updated, as per the first comment under the video.

Do yourself a favor and grab more than 10 practice cannonballs! The cannon costs 10 energy to borrow, and then each 10 cannonballs is another 10.

Go to the platform on the castle where it leads you. You'll have to climb onto the broken castle wall and drop down from above, and there's an interaction point named "Blocked Path" where you need to. Set up the cannon, load the cannonballs into cannon inventory, and fire at the practice dummies in the water; they're slightly short of and to the right of the sea monster. If you can't see the dummies, make sure your graphics are set for a long enough range and to show distant objects better and so forth.

The cannon will only last 10min before collapsing, and can't be retrieved, so don't waste time once it's in place. A red beam will appear where you hit. You want the LOWEST angle and about 10% charge (err on the low side). Thankfully, you don't actually need to hit an individual dummy, just the area they're all in.

The only way off the platform you're on is down - expect to suffer some fall damage, but it won't kill you to land at the base of the castle wall.