Sunset Overdrive

After one of the story missions you will be able to destroy Fizzco Blimps that fly above the Sunset City. Instead of running around and looking for them you can easily blow up 25 blimps using Glider Challenge #1. Start this challenge, ignore mines and destroy blimp right away. Now press Menu button on your controller, then X and abandon challenge (if you restart, blimp won’t reappear). Repeat every step until you get your achievement. Check video below if you have problems.

Much faster than other method. Fast travel to "Oxfords Base", once you arrive, head to the right and climb up to the higher bridge. There will be a blimp just above your head, shoot it down with whatever weapon you like, then fast travel back to Oxfords Base and the blimp will respawn. Please check the video for detail.

Both of the above solutions are great but this is how I got this chevo.

Go to the Glider Challenge number 2#, accept it and right after start of that challenge and you will see a blimp right ahead of you but you will notice that it is somewhat far away. Instead ignore it for a second and make a 180 spin and you will see a second blimp just right behind you. Destroy that first and then go for after that first saw blimp. Yes this challenge has 2 blimps instead of one !

After blowing up those 2 blimps, just crash you're glider to the ground and accept continue (press button). You will then re spawn right next to that challenge marker and those blimps will re spawn too. Accept that challenge again and just rinse & repeat afterwards.

Hopefully this one helps, cheers !

Edit 1: Instead of 360 spin, it is now 180 spin. Thx for RAVIOLICAPONI for correcting this.

Little extra tip from CHUCK NO7715; " - instead of simply crashing each time to respawn/restart, have a look around the area and look for Fizzco neon signs or Fizzco balloons and glide through those also. Helps bump up the numbers on collecting these items at the same time as notching up the blimp destroy task."

Video showing the below coming soon.

The blimp appears 100% consistently with this method, regardless what point you're at in the campaign (including the part where they stop spawning, after Wingers start appearing IIRC) and I believe it to be slightly faster than the Glider Challenge methods. (Plan on timing it.)

You need to be at the point in the story where you meet the larping group.
The one member that only says his name "Hardcore" will have a quest for you.
Accept it.
Little prep work needs to be done. Destroy all the boxes/objects till you get to the next part in the tennis courtyard. Should take a minute or so. Prep work done.
Grab the cross bow in the tennis courtyard, you don't need to move your character, just the aiming reticle for now. Shoot the two barrels that get launched into the air. Next shoot barrels in the air once they line up with the flock (group) of birds that fly by. Shortly after Fizzco planes should start flying by, shoot those too. After a short while again UFO's will start popping up, shoot those. Once you fill up a third or so of the bar in the upper left (underneath where your gun is) if you turn your character to the left, you should see a Fizzco blimp. The blimp always comes at the end, shooting it will end this segment and go on to the third part of this quest but you do have enough time to leave the little yellow area on the map (basically climb over the tennis court wall and run a little) before the save icon pops up and you will fail the segment and start from the beginning where you have to shoot the two barrels and repeat the rest of the process.
I suggest you have the achievement app snapped so you can make sure the blimp progress is counting, I would wait a second after shooting it to see the tracker go up before jumping over the tennis court wall.

This is the method I discovered and it worked well for me (wish I had found it before I had repeatedly chased several blimps half way across the map)

You will need the slam jump ability, a 'standard' gun and access to the third (I believe) 'island'/area (I did it after finishing the story)

Fast travel to the Shipping Yard - a blimp will spawn above you and to your left, with the slam jump you can get high enough to shoot it down with out any climbing or traversal needed

Once you have shot the blimp you can then just fast travel back to the Shipping Yard (even though you are already there) and the blimp will re-spawn - rinse and repeat