Got no idea about the battery water, but seeing that battery water is caustic, I don't think that its a good idea.

Acrylics r best mixed with distiled water (although tap water will do just fine). The detergent is to reduce the liquid tension of water, allowing for it to flow better, but the mix ratio is just to use a tiny tiny bit of detergent. If it can form bubbles when u shake it, then u've added too much.