Takes place in Nassau
Gunpowder Keg 1
Head to the closest marker to the South. Look for the edge of the Restricted Zone around the gunpowder. There are 2 Brutes guarding the entrance. Equip the Berserk Darts and tag each of them with one. This will draw some of the nearby guard in and pull them away from the entrance. Wait for the Brutes to be killed and the other soldiers are leave. Kill the last one with an air assassination to drop to the ground quickly and safely. Head inside the passage the brutes were guarding. Rush in and kill the Scout who is standing a little ways down. Go over to the Corner and take up a position there. Watch the Scout and Brute. When their backs are turned (or they're behind the crates), dart over to the Stalking Zone on the left-hand side of this tunnel. Kill the Scout when he goes by and the Brute isn't looking. From there just deal with the Brute. Look around the crates to find the first gunpowder barrel.
Gunpowder Keg 2
Head out of the tunnel through the other end. Slip out past the guards (or engage them) and go to the East. There you will find the second Powder Keg under watch. To get in quietly, go to the nearby staircase to the South of your location. grab onto the ledge an sidle along it. Pull yourself up when you make it to the overhanging rock. Dart from there to the nearest Stalking Zone to the East. Slip in toward the marker. Deal with the Guards using Darts to make your life easier. From there just go into the tent with the Gunpowder and steal it.
Gunpowder Keg 3
Head to the Southwest and approach the next keg. Deal with any resistance as you would like. There is no penalty to just killing all the guards. The easiest way is to slip up to the Restricted Zone through the sugar cane Stalking Zone by it. This puts you right by the keg you are after with one a few guards around it. Tag the nearby ones with Sleep Darts. Slip in from there and claim the keg. Just slip right back out again after that.
Gunpowder Keg 4
Head over to the West. Get to the Northern end of the final Restricted Zone with Gunpowder inside it. Pick off the Scout wandering the area. After that just watch the other Guards for an opening to slip in. There is only a Captain and Scout patrolling the area so it is not too hard to deal with. Tag them both then head in to steal the final keg.