This achievement requires you to finish in first place for 60 arcade chapters. One of the easiest ways to do this is to sign in a guest controller, and then play arcade on the prologue mission (Act 1, Chapter 1). This level is much shorter than chapter 7 in act 2, and in addition to that, you can't even die or take damage (as far as I know), so difficulty isn't that important (I did it on casual to be safe though).
Just play that level and once it goes to the next chapter, back out to the main menu, then rinse and repeat for an easy achievement. Reloading the checkpoint is faster than backing out to the main menu.
Also, just in case anyone is wondering, you MUST either have a guest signed in or someone playing with you to get the ribbon. Playing by yourself will not work.
EDIT: I've added a video, it was made by Lucid Dreams84 (he also sent it to me). Thanks man!
VIDEO NO LONGER EXISTS. REMOVED LINK. Reported Content Team.
***You can also use this method to farm points for the king of cog medal (where you have to earn points in arcade) by putting the game on insane and putting on any hard mutators (such as friendly fire and no ammo pickups). No ammo pickups is a good one to put on because you have unlimited ammo for this level. (It may also be a good idea to put on super reload, and then combine that with some hard mutators, just to speed up the process). This is also a good way to farm Aficionado (play a certain amount of chapters of arcade). Chapter 7 in act 2 is actually the best chapter for farming points, and you can get an easy 10X multiplier, but do the prologue if you are going for both king of the cog and Aficionado***