Skylanders Giants

To get this achievement, you must not take any damage from the gun turret mini game. I forgot when you unlock it, but when you do, it's near the bottom left of the ship.

Anyway, when you play the game, you'll have to shoot down something random, like rockets, barrels, or sheep. Keep playing until you get to shoot down artillery shells, which are Kao's rockets.

You must hit 30 of them WITHOUT taking damage. If you get hit, then let the shells kill you until you die. You can restart and try it again until you get it.

Tip: When you do get to shoot down the artillery shells, DO NOT leave that part of the ship until you get it. If you leave, you'll have to keep playing until you get it again, because what you get to shoot down is always chosen randomly.

If it's too hard, use a Tech skylander. I used Drobot if it helps. Also, if you keep dying, it should make getting the achievement easier to get. If the shells come from the middle of the screen rather then the sides, then you should be good.

Edit: According to FailedSeppeku, Skylanders form the Wind element are the best to use.

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I just want to add to these solutions that if you have the time-twister hourglass you can use that to slow down time, and get this easier.

After doing some campaign chapters you can descend down the available hatch on the main deck to access the gun turret mini-game.
Now my advice is to play the mini-game until you get the Rocket Artillery mini-game as there are three variants Rockets Barrels and sheep.
Now if you get hit simply let the rockets finish you off, as this will allow you to press Y to replay the same mini-game without you having to exit and re-enter which then makes the mini-game given a lottery again.

Rinse and repeat until you destroy 30 rockets without sustaining damage and this achievement is yours!

Hope this helps :)

Quick Version:
If you have any friends (and 2 skylanders), you can simply plug in a second controller and have them cover one 1/2 of the screen while you cover the other. It was trivial to beat without getting hit with 2 people.

More information to be thorough:
After Chapter 7 you will be able to go down a hatch on the Dread-Yacht (directly right from where you start on the Dread-Yacht) to access the gun turret minigame. There are multiple possible minigames (shooting down sheep, barrels or rockets) and the one you want is the artillery shells.

I found that the minigame did not change by reloading a chapter and quitting, or exiting to the main menu. Only beating (or possibly replaying) a story chapter would change the minigame.

As the other solutions state, once you get the artillery minigame, you can simply let yourself die once you are hit that way you can keep trying for this achievement if you mess up. If you finish the minigame while being hit, you will have to wait to get the minigame at random again.

As SockHead999 points out, wind and tech skylanders are the best choices. I didn't have the time-twister hour glass as Cronis the 1st points out, and I tried to beat this minigame 30 times by myself with no luck. It seemed impossible.