The Gatling Gun/Rocket Launcher is an idle weapon that overthrows the role of the Ballista/Flower Cannon. Usually the Cleric is able to throw down materials needed for the former weapons, but the Engineer is the only class that can upgrade these weapons to the latter.
While this achievement can be done with any class, the fastest way to get 100 builds is to play as the Engineer, which is the only class that can lay down the materials needed for either the Gatling Gun or Rocket Launcher using the Update skill. Of course, building the Gatling Gun is slightly faster.
You are allowed to build and destroy on the same spot, so the safest way would be to stay in your castle. However, if more than two people are building, you may not get credit for that build yourself. You'll know if it counts as you'll get 25EXP for each successful build. Use Crash Work in conjunction to get more builds per match.
If you do nothing but this for the whole 15 minutes, it should only take around five full games to earn. Remember to watch out for bots!
Thanks to Masta Skor 16 for collaborating together on this!
Update: If you want this faster without having to wait for it as a skill while leveling up in-game, you can now add Update+ to your equipment as a buff. As of yet it's only available through Happy Cards. Thanks to lightsup55 for the details.