Ring of Pain

Bilebags are creatures that shoot you if you get within 2 spaces of them.
Best bet to kill one from a distance is to look for items that deal damage to random creatures under certain triggers (for example items that deal random creature damage when you attack)
With one of these items equipped, find a dungeon with bilebags and kill all the other enemies so that the random damage will eventually kill the bilebag. Just make sure you are far from the bilebag when making kills, leave as many items in the ring as you can to keep your distance

Alternatively. there is a spell scroll you can find that spends all your souls and deals equal damage to random creatures. Use this in a dungeon with bilebags, preferably when there are not many other monsters around as you could still get unlucky and it not hit a bilebag

Achievement doesn't state what distance away you need to be, but I think it means out of range of their range attack. If you can see a yellow damage icon on your health bar from the bilebag you are targeting, then you are probably too close