Deal with the Bandits is a story-related quest in Act 2. The outcome you choose is tied to this achievement. You can either help one of the 3 bandit lords (kill the other two), or kill all 3 of them. For this particular achievement you need to help all 3 bandit lords at some point during your game.
You can play 3 different characters up to Act 2 and help a different bandit lord (Kraitlyn, Oak, Alira) or you can use a special vendor formula to change your mind. Any combination of these works fine as each vendor formula or bandit you help you will see the challenge progress appear in the bottom right corner. I personally helped 2 bandit lords with different characters and changed my mind with one of them.
The vendor formula is expensive, so playing with 3 characters is certainly the cheaper option, but if you want to change your mind late-game, the formulas are:
20x Orb of Regret + Jade Amulet -- Gain Kraitlyn's Favor
20x Orb of Regret + Lapis Amulet -- Gain Alira's Favor
20x Orb of Regret + Amber Amulet -- Gain Oak's Favor
20x Orb of Regret + Onyx Amulet -- Gain 2 Passive Skill points (kill all 3 Bandit Lords)
Killing all 3 Bandits is not a requirement for this achievement, but it is usually the preferred outcome.