"First Blood" awards are earned by making the first kill in a match. You can't state it more simply than to charge at the first enemy you see, guns blazing, and take him down.
With all the grind Achievements in this game, it should come naturally over time, but if you find it eluding you, set up instant action matches with a single Novice bot and you should be able to easily take him down first. Setting up low requirements for the match will make the matches progress faster, though if you set them too low they will not count toward some of the other Achievements (many of which have a 20-kill minimum).
The Achievement will unlock as soon as your 40th "First Blood" award is earned (as opposed to at the end of the match containing said award).