This is very similar to this other achievement, but with a big difference:
You just need to get ONE of each type rings this time! a +1, +2, +3, +4, OR +5!
BY FAR THE EASIEST AND BEST METHOD IS SIMPLY BUYING ONE RING OF EACH TYPE OFF THE AUCTION HOUSE!!
At current time, 4 of the rings are less than 3k AD each, and the Dinosaur Slayer ring is coming down under 20k now.
Just search the Auction House for rings and use these keywords and buy one of each ring, +1 or +2: (you can also set the optional setting to show ONLY rings with 2 slots to further narrow things down)
Note, the Hunter rings are not required for this achievement!
Otherwise, the hard way: