UPDATE: After the latest update, this solution will no longer work due to the changes in how villagers trade. Thanks, Mojang! If anyone has any ideas, please leave them in the comments and I will update the solution accordingly.
Aco2148117's solution is great, but I just wanted to share another good seed I found for those who don't want to walk the 20k+ blocks required for his forest mansion :)
The seed number I found is 667503609. Very close to the starting point, there is a village with 3 cartographers (!) and 2 librarians (which I believe have a chance of spawning as cartographers?). The village is located at 191, 64, 304 (there's a temple nearby with some goodies at the bottom as well). Of the three cartographers, I decided to trade with the one whose first trade was for 25 pieces of papers. (The other two were 26 pieces of paper and 30. I'm cheap, so the choice was obvious.)
His full trade path goes:
25 paper for 1 emerald
1 compass for 1 emerald
9 emeralds for 1 empty map
13 emeralds + 1 compass for 1 ocean monument map
(He also offers a forest mansion map for around 26 emeralds, but I was impatient)
I traded him up a few times with paper, then traded him 5 or 6 compasses to level him up enough that I could bypass the 9 emeralds for 1 map and go straight to the ocean map. If you're looking for a good cave for the iron and redstone needed for compasses (not to mention a good amount of coal), I dug a hole literally straight down at 92, X, 154. (Craft a bunch of ladders first so you can climb back out!) Once you're deep enough (I stopped at 92, 12, 154), make your way toward a couple blocks of diamonds located at 102, 11, 167 (watch out for the lava!) and you'll find plenty of redstone and iron along your path.
The ocean monument isn't too far away, but you'll probably want a boat to shave a few minutes off your time. It's located at 2632, 62, 1735. Pack a good stack of food, some ladders, and some cobblestones (the latter two for building a tower on top of the ocean monument to dig straight down into the Elder Guardian's room) and start heading southeast until you get there. Once you're there, dig down into the monument as I mentioned and the achievement should pop after a minute or so of swimming around and coming back up for air. (I was holding the map in my right hand, not in my shield hand. Not sure if it matters.)
Hope this helps! If you have any questions, please feel free to DM me here or on XBL and I'm happy to assist :)