Launched in Space is the first event in the Space Frontier booth in free play. It's unlocked from the start so the easiest way to play it is through free play, or you'll get there eventually in Adventure Mode.
First tip: Holding down the right trigger will rapid-fire. Basically just hold it down the entire level.
To open the window in the planet that Zurg is hiding in, you first need to shoot all the green and red balls on the rotating rings around the planet at the top. You have to wait for some of them to come into view. Once all the balls have been hit, four planetoids will pop in from the bottom. Hit all of those and the window will open and Zurg's head will appear. Just keep firing at it. You may need to do this twice in a level to get 30 shots, but it should be quite doable.
Once you've shot him 30 times the achievement will pop immediately.