Nothing but tears

beat me to it

No. It means it won't hurt the baby's eyes if the shampoo gets into them. I don't know if this confusion is real or simply trolling, but I can remember when the "No More Tears" commercials first came out and they definitely mean tears as in teardrops. I believe Johnson and Johnson even confirmed this awhile back.

it was advertising ploy by the mispronounciation of the word "tears", when it meant not more tears, or torn hair

Nope, guest is right. It's tears because its baby shampoo that is so sensitive it won't sting if it gets in baby's eyes, thus not causing baby to cry and hate bath time.