This refers to the red goblin hanging from the balloon in several levels. This is probably easiest done on Level 2-3 where you use all Flying Shots. After extending your wings, simply fly directly at the red goblin - not the balloon above him! Once you smack into him, he will ride piggyback on your flying bomb (kinda like Slim Pickens did in the movie Dr. Strangelove but your goblin will be facing forward). Use Mulligans or repeat this level until you accrue 30 goblin rides. You can have him ride any type of bomb on other levels with balloon goblins, but I feel Level 2-3 is easiest if you're trying to farm this achievement.
I couldn't find a video of someone doing my suggestion, but look for this Bomb Shot example at about 1:20 in this advanced video from the developers:
here's Slim Pickens' ride: