To expand on other tips...
90% of the time I get the pirate 8 times per screen, unless I accidentally mess up.
The first two times I get him from the bottom, all others from the left - 9 o'clock position. To start, I shoot straight up to clear a path, then move over to one side to get a 'single' mine (not all the way over, but a low, single mine). The pirate is exposed at 6 o'clock. Then after shooting the pirate, I shoot the 2 clusters of 3 mines at the bottom, along with the counterpart 'single' then the pirate again.
After that, I slide up the right side and ONLY shoot the stuff to the immediate right of the pirate, including 2 mines. After this, slide around to the other side of the screen, shooting NO mines along the way, then shoot out the left of the pirate, the go up shooting 2 more single mines or the double at the very top. This should give you another shoot at the pirate on the left.
From here, you can pretty much see groupings of 6 mines. Every six you shoot, he'll be exposed for you
I find that if I try the same method each time, it becomes smoother with less panic.
Along the way, you'll find certain dots that can only be shot from the bottom. Be sure to clear them before making your way to the left side of the screen. There are a couple dots that can be left for your last shot to clear the screen. Pick a favorite and make it be the last every time.
Too wordy? Too much rambling? I dunno...maybe someone will follow and find be helpful.