This achievement is getting to Level 20 in Arcade Mode (Map Creator / Multiplayer). It only takes a few hours (between 2-4 hours). You can do this in solo, co-op, or MP arcade. I strongly recommend you do this in MP as a) you will need to play a lot to get ARCADE Competitor and ARCADE Hunter, to the point where this will probably be earned through natural progression, and b) you will get a 20% XP boost with a win + more initial XP in most cases playing MP > Solo/Co-op.
Aside from that, just play Arcade mode and you'll get this naturally. The only thing to note is as of 2nd April 2018, please be warned that there is an unknown glitch causing people to lose progress. I got to Level 12 by playing for fun, came back after getting all single player achievements and my ARCADE level was reset to 1. Ubisoft are aware of this, and there are workarounds so don't fear; a) do it in one session (set some time aside, a weekend..a day off..etc.) or b) Don't exit Far Cry 5 if that isn't possible. If you want to turn your Xbox off, put it on the off mode which allows you to resume progress and not a complete hard reset.