A easy way to get this achievement is to distract Madame Von Bartlesby and then attack her from behind. Halfway up the narrow path, buzzards will rise from the Buzzard Academy. A few shots in that direction should attract them and Madame Von Bartlesby will engage with the buzzard giving Vault Hunters necessary time to finish her off.
Another way is to spawn Madame Von Bartlesby, jump off the cliff and then snipe her from a distance.
Madame Von Bartlesby occasionally release these bombs which follow a long curved path before homing on their target. If Vault Hunter gets hit by a bug bomb after Von Bartlesby is dead, they'll still fail this challenge.