This can be done on a regular character or a hardcore one. If you want to make this much easier, do so on World Tier I, as the enemies will be easier to kill.
When you start off the game you will be poking the bad guys with the business end of your daggers, which count towards the melee range part of the achievement. You should finish the rest easily as kills with your bow count when the baddies are an arm's length away.
You should probably pop this one by the time you reach level 7 or shortly thereafter. Just keep killing things with your bow. A number of enemies will get in melee range even when you switch to ranged attacks and those kills will count.
