What tool should I buy to cut through very hard plastic?
When we cut vinyl siding, my tool of choice is a circular saw with the blade installed backwards. By putting the blade in backwards, it will wear down the plastic with a smooth line rather than shred it with a rough edge. The thicker and harder the plastic, the slower you have to go.

If the circular saw doesn't work (perhaps because you can't make your cut as a straight line around the rim of the barrel) then a Sawzall is the quick way (I'd be tempted to use a blade with a high tooth count to reduce shredding). And if all you need is a small round hole, then your standard hole saw on a drill will work.