How good does your vision have to be in order to pass the test for the ame?

Standards below. Current standards are: for 1st & 2nd class: distance of 20/20 & near 20/40 at 16 inches (if over age 50, at 16 & 32 in) in each eye with/without lenses and full visual field. For 3rd class, 20/40 at distance and near at 16 inches (any age). If lenses are needed, this will be noted on your faa certificate. Some color vision issues are present. See: ecfr.Gpoaccess.Gov.
See below. According to the faa and 14 cfr part 67, for 1st & 2nd class airman: distance of 20/20 & near 20/40 at 16 inches (if over age 50, at 16 & 32 in) in each eye with/without lenses and normal fields of vision. For 3rd class, 20/40 at distance and near at 16 inches (any age). If lenses are needed, this will be noted on your faa certificate. There are other stipulations as well. See ecfr.Gpoaccess.Gov.