To unlock this you must complete level 2-4 without triggering any looters. Restarting from the nearest checkpoint will not reset this achievement, you'll have to go back to the map and restart. You'll know the achievement is voided if the loot counter in the upper left corner changes to the danger graphic with swords and red eyes.
The chariot attracts nearby looters by making noise, either by hitting an object at high speed or by collecting gold/gems. Level 2-4 (The Hive) has plenty of looters, but they are all centered around the actual hive, a spire in the middle of the map which you approach five times throughout the level. Making all sorts of noise in the rest of the level, including all bounce pad sections, is fine and not a problem.
I recommend using the Attractor if you have it. Just don't use it anywhere near the central spire and you'll be fine.
EDIT: If you have the Royal Gadget DLC, try using the Stasis Field gadget to pause the chariot's motion. 'Panthera onca' recommends this approach.
The first place with looters nearby is at the end of a downward-sloping death rail. If you do nothing, the chariot will hit the wall at the end and disturb them; hold left and
continuously to slow the chariot enough for a silent landing. Then climb carefully up and back over to the left.
The second place is shortly after that. You'll make your way over platforms back to the hive area and have to climb up next to a looter hole. If you have the Attractor you can stay away and boost up to the higher platforms, otherwise just avoid pulling the chariot up onto the rightmost ledge where the gems are. If you don't collect any gems you won't bother the looters.
The third place is after the first bounce pad section. You'll go down a ramp and off a jump; if you jump here you can land on a life path and skip the looter area.
The fourth place is the most risky. You'll ride a much faster death rail down from the top left part of the map; the rails zigzag down and then across the top of the looter hive. There is a purple gem just underneath the rails here; it is imperative that you do not let the chariot stop long enough to collect it. Move quickly past the tip onto the nearby life paths; anchor and reel the chariot in. Continue this until you're up and away from the looter area.
The fifth looter area is not so bad and can be completely avoided. You'll come down another death rail from above; hold right and
to slow down as much as possible. When you get past the death rail slowly descend on the right side of the cavern until you get to the section with life path platforms. At this point you're in no danger from looters; proceed to the end of the level for your achievement!