Find general intel on Legion troop movements and Legion raids in Cottonwood Cove. This can be done through conventional means, or a truckbed atop Cottonwood Overlook can be opened with a Lockpick of 50 to release the radioactive barrels.
(Optional) Give First Sergeant Astor the old intel. - Caesar's fame
Return to First Sergeant Astor with the intel.
Kill all Legionaries in Cottonwood Cove
Return to First Sergeant Astor
It is best to wait for all the barrels to fall into the camp before fast-traveling back to Astor talk. If you open up the truck, but fast-travel to Astor too soon, then the game doesn't realize you've killed the legionaries using the radioactive waste.
You will incur no reputation loss for dropping the barrels on Cottonwood.
If you tip the radioactive barrels into the cove before completing the quest Left My Heart, you will fail the quest as the Weathers family will die from radiation poisoning.
If you decide to drop the barrels on the Legion forces at Cottonwood Cove, you will still be able to use the ferry to reach Caesar's camp. The Legion ferryman, Cursor Lucullus, will now be wearing a radiation suit and will still grant you access to The Fort.
"Eye for an Eye" is a well known phrase dating from the times of Hammurabi. Known as Hammurabi's Code, the laws dictated an "eye for an eye, a tooth for a tooth", meaning that any law broken, or anyone harmed, the perpetrator would receive the same as punishment.
PCXbox 360 Sometimes dropping the radioactive barrels will not kill all the legionaries. They will remain standing in front of the barrels without ever succumbing to the radiation. Four legionaries line up at the base of the cliff while the barrels roll right through them. However, the objective is still marked as complete in spite of the fact that the survivors can still be killed, V.A.T.S., and otherwise interacted with.