Yes, it's "1-A" by Thomas M. Disch, 1968, originally published in New Worlds #181. I read it in the Disch collection Fun With Your New Head; it's also in another Disch anthology, Under Compulsion.
The four things are "loyal, courageous, self-controlled, and dead."
(Edited: here are the final pages of the story - abridged because the Captain does go on for a while. This happens after the main character has gone through various induction experiences, including the barber that the question mentioned, and read a bunch of inspirational stuff from the Field Manual.)
"Now, some of you may be asking yourselves--what makes a good soldier? Well, I don't pretend to be any philosopher, ha, ha, but just offhand I'd say that a good soldier is loyal, courageous, self-controlled, and dead.
"What do I mean by loyal?
"By loyal I mean that a good soldier loves his country. ....
"What do I mean by courageous?
"By courageous I mean that a good soldier is brave. He does his duty no matter what hazards arise. ....
"What do I mean by self-controlled?
"By self-controlled I mean that a good soldier knows discipline. ....
"Lastly, what do I mean by dead?
"In just a minute I'll show you what I mean by dead ... but first let me say, off the cuff, that I think this company is going to be the best goddamn company in Fort Candler ...."
After Captain Best's speech, and after the cheer for "A" company, a curious and very large vehicle, which moved on treads, lumbered up the gravel parade grounds .... at regular intervals around the shell there were apertures from which the nozzles of small-caliber guns projected.
The captain raised his right arm, then brought it down sharply.
The guns ... commenced to fire upon the men of "A" Company. They continued firing until all the men had been lying on the ground, either prostrate or supine, for some time. ....
"Now that," Captain Best said with satisfaction, "that is what I mean by dead."
