Below is the cover for the second print of Batwoman #1. All second prints of The New 52 are identical to the original runs with the excetion of a red tint on them. For the cover of Batwoman #1, these changes are very subtle, but they are there. The color of the logo is different, the added red background behind Batwoman's head, and the steam color is grey where before it was kind of greenish. You can check the original cover and compare. I wish DC had decided yo go for different covers altogether; it would have been an excellent opportunity to showcase Amy Reeder's variant covers.
Batwoman #1 Second Print Cover by J.H. Williams III
Earlier this week we saw a preview of Batwoman #2. Here is another spoiler-free preview, this time with colors by Dave Stewart. Chapter two of "Hydrology" is titled "Infiltration". Hey... is that Batgirl over there? The complete preview is over at Entertainment Weekly.