This is a two-part achievement, but you don't have to do them both in the same match. I did this in the Campaign.
When you're in the Everglades, head out of the ring and look under the ring until you find a motorcycle - you'll be using a Brawler, so if you like you can use
, and sometimes you end up with a motorcycle in your hands
You can destroy the ring in a number of ways, but the easiest way to do this is to wait until you're in Detroit, where you have a character who can pick up the ring post. There can be a barrel that appears in the bottom left corner of the ringside area; pick up the barrel and place it right by the apron. Wait for it to explode, then head out and pick up the post that's on the ground
You can also get this in the Exhibition modes too, when you've unlocked the arenas - using a Brawler in Detroit can get them both done at once
If you do downvote this solution, please explain what needs improving and I'll edit the solution