Does completing a mission in Brutal difficulty counts towards the "Wings of Liberty: Hard 5/10/15/20/25" achievements?
Solution 1:
Yes. Any achievement, any achievement, that has a difficulty requirement as part of the achievement can also be completed on a higher difficulty. This means that (if you're good enough) you can get all of the Wings of Liberty Mission achievements on a single playthrough.
E.g., for the Red Lobster achievement, you can taunt the Brutalisk into the lava on Normal, Hard, or Brutal -- you don't "have" to be on normal (despite the listing to the contrary)
Solution 2:
It does count indeed.