ANIMAL WELL

I'm not entirely sure how many secret rabbits there are, but I found one pretty early in the game (in the first hour). To reach it, head left from the central animal statue room into the seahorse area. If you've already explored that area, you're targeting the large bubble-filled room shortly into this area. Head to the bottom of it where the fish are releasing bubbles, and exit the upper right side of this lower room. From here, you'll need to follow this path past some angry cranes that try to peck you. Personally, I literally only had the bubble wand at this point but was able to platform my way across. You'll then need to go through some spiked areas. This again a little tricky with just the bubble wand, but fully possible (I did it). You'll then finally reach a room with a rabbit you can startle to unlock this achievement.

As a side note, the intention is definitely that you would get the B.B. Wand, an upgrade to the bubble wand which lets you spawn bubbles infinitely, and use that to get through the spiked wall area, but as I said, it is fully possible with just the bubble wand (refer to my FAQ link in the roadmap to find out how).