You need to get a little lucky for this one. The only way I've found to make a hero drunk is to look for one that has the Reveler personality trait, which will make them drunk at random times. You then need to be lucky enough that they're actually drunk when a battle comes along. If they are, it will simply say Drunk on their status page. This decreases some stats (mainly accuracy), but getting 5 kills still shouldn't be much of an issue with the rest of your vanguard backing the drunk person up. The achievement unlocks as soon as the fifth kill is made.