What this achievement means by "Complete" is not do every mission. Its actually just to complete the last level, "Final Showdown".
This can also be done in co-op contrary to belief. The catch is that only the host will get the achievement. So you will have to do it again with your partner being host.
Essentially what you could do is find someone who has the achievement already, have them do the second to last level "Boardroom Blitz" with you, and then do the last level "Final Showdown"(makes sure your host if playing co-op), without having played any of the other arcade levels.
[Boss Tips: "Dude on The Horse"]
The boss will come in 2 stages.
- First he will attack on his horse. You will need to press B right as he is about to hit you about 4 times.
- The second he will attack on the ground. When he jumps/teleports, use the arsenal and air juggle him in the air. His health will go down real quick with that.
- Also remember that when you co-op partner dies, pile drive a few zombies, and that should bring him back to life.
Thanks for reading, hope you the best of luck.