I would recommend creating a save before attempting this. You will want to ensure you have at least one bunny left in your inventory for the Rabbit Ragu achievement at the end of the game.
After you have stolen the box of bunnies (see Invasion of the Bunny Snatcher achievement), head back to the minefield. Once there use the bunnies on the minefield. Ben will back up and release the box. Immediately use your hand and gather all the bunnies before they explode. Once you have all the bunnies, walk as far towards the minefield as it will let you. Then use one bunny on the minefield. The bunny will advance a little bit and explode. Move Ben up further along the detonated path and use another bunny. Keep repeating until you have advanced far enough to get to the Vulture hideout entrance. If you don't advance up enough after each explosion and all your bunnies are gone, you will need to steal another box from the gift stand and start the process again. Just head back there and grab another box. Horrace is not manning the booth. Once you have advanced far enough in the minefield, a cutscene will start and the achievement pops.