The best way to do this is playing a co-op game of 2 players on easy difficulty. Do not change any additional options in the menu or it won’t work. If you play with 2 other players, this means a 3-player team, the map will be bigger, and you will have to build more walls, also the enemy waves will be bigger.
I think the best way to do this is having one player focusing on creating units (I recommend air units, but other units also work well) and expanding in the map, while the other focus on collecting supplies to build walls (he/she can also help with some units, but don’t create a big army).
When the game begins, stay and protect the starting area (Terminus and main bases). Build walls and turrets and start building a good economy. After wave 6-7 when you and your friend have supplies and an army, go and dominate one of the unexplored sides of the map, building the bases, walls and turrets. Don’t stop training units to defend your bases against enemy waves!
Once you have that zone controlled you can make your way to the other side of the map. Now just use all your supplies to create walls. Once you built a wall in every slot the achievement will pop.
Edit: I can confirm that any type of wall counts for the achievement, as long it's construction is finished.
NOTE: It seems like any type of wall counts for the achievement. When I did it, I used different type of walls, including Banished-UNSC walls, and the achievement popped.