Pretty self explanatory. Kill multiple dudes in a short time span. Repeat 249 more times.
I picked it up without trying after playing through on hard and then replaying 5 or 6 levels for ceo.
If you want to boost it, I'd recommend getting the Killing Spree chip upgrade (Rampage timer lasts for double the time, and kills during rampage have increased damage by 25%) as soon its available.