Will Blink 2 (II) prevent me from getting the achievement Mostly Flesh and Steel?

Someone has reported (Reddit - /r/dishonored) that getting Blink II will indeed stop the Mostly Flesh and Steel achievement from unlocking.

Another report (also from /r/dishonored).

Also, from the "Notes on Stealth Detection, Chaos, and Trophies/Achievements" post in the Bethesda forums by Gstaff, an admin and 'Global Community Lead':

I did not receive the ‘Mostly Flesh and Steel’ Achievement/Trophy despite only using the Blink supernatural ability. Why?

• The description reads “besides Blink,” however, this is referring to the initial Blink power that you receive from The Ousider in the Dream. Purchasing Blink Level 2 will prevent the Achievement/Trophy from unlocking.
• Equipping Bone Charms will not count against this Achievement/Trophy.

You didn't get the achievement because you upgraded from Blink I to Blink II.