Treasure Goblins are the small, glowing creatures carrying a purple sack that will scurry away and open an escape portal if you come too close. On your mini-map, they're show as a fat white dot with a small blue filling. You need to kill one hundred of them for the achievement.
Now, don't rely on the xbox tracker to see how many you've killed, instead use the in-game challenge list. It's located under 'Thriumphs'. It's quite slow to update, but nevertheless reliable.
The good news is, all goblins killed with all characters, in all modes (be it normal or hard core, campaign or adventure) count. The bad news is that patch 2.1.0 has made them hard to find, as numerous potential spawns have been patched out. Also, the previously excellent Puzzle Ring doesn't seem to be working as before, at least it did not for me. The new 'portal goblins' and 'treasure fiends', while looking like 'treasure goblins', apparently don't count, but of course there's no reason to not end their lives.
While they can spawn anywhere, I found two reasonably effective farming spots I used while grinding 500 bounties. These locations merely have a higher chance to spawn goblins, meaning you could go through them ten times without seeing a goblin - I know I did. But that is sort of what you'd expect from a game like this, right?
Location 1 is the 'Royal Crypts' area, right before the Skeleton King in Act 1. The area is small and the layout is always the same, so including loading times and teleporting, a fast-moving character can check the dungeon in about two minutes.
Location 2 is also in Act 1, and it's the 'Caves of the Moon Clan'. This dungeon actually spawned more goblins for me (in rare occasions, even two in one run) but it's larger than the crypts, and both layout and location are random each time. I suggest you pick up the correspondig 'clear' bounty when heading there, as you'll be anyhow scouring every corner in search of the elusive goblin.
I hunted down 84 of the required 100 in these two locations. I played both on hard in hardcore mode, but mostly normal mode on Torment I & II. On a side note, I got the rainbow portal three times, and the treasure vault portal four times.
Happy hunting!