Tl; dr: It will take approximately 3,000 matches, on average, to get this achievement, until the game runs a Treasure Gnome event which will increase the odds significantly, or you gain a key from a raid boss event.
This achievement is for winning a "Gnome Vault" battle.
The Gnome Vault is accessible via the "Games" tab. In order to play a Gnome Vault battle, you must first obtain a vault key. It costs 1 vault key per Gnome Vault battle attempt.
The hardest part about this achievement will be obtaining a vault key. Vault keys are currently only obtainable as random loot from Treasure Gnomes. Treasure Gnomes are new troops released with the 3.3 update that have a chance of randomly replacing an opponent's troop any time you start a battle. You can quit out of a match immediately after seeing a gnome didn't spawn if you wish, but finishing the match (on easy difficulty at least) will likely be just as fast.
Currently, Treasure Gnomes have low chance of appearing (update: now approximately 1 in 30). Treasure Gnomes can appear in most types of battles except for Guild Wars, Tutorials, Training Battles, and The Vault. One of the developers posted in the official forums "Spawn rate is equal over all modes that can spawn gnomes. Difficulty setting does not affect spawn rate."
If you are lucky enough to have a Treasure Gnome show up in your match, do your best to ensure that it does not have a chance to cast its spell. From the official 3.3 patch notes, "Both the Treasure Gnome and Valraven have a new spell effect as part of their spell called ‘Run Away’. This allows them to run away from the battle, meaning their reward will be lost if they are not defeated quickly enough."
If you manage to kill a Treasure Gnome and win the match, in the end rewards you will get random Treasure Gnome loot. The possible Treasure Gnome loot reported in this information gathering thread ( https://community.gemsofwar.com/t/after-gnome-rebuff-and-rew...
) so far appears to be:
5 Gems * 36
20 Gems * 8
1 Gem Keys * 13
4 Gem Keys * 10
1 Event Keys * 9
3 Event Keys * 8
2 Diamonds * 13
5 Diamonds * 15
100 Souls * 45
200 Souls * 2
500 Souls * 10
2,500 Gold * 48
4,000 Gold * 27
6,000 Gold * 8
10,000 Gold * 5
20,000 Gold * 7
30,000 Gold * 1
50,000 Gold * 2
60,000 Gold * 1
2 minor traitstones * 22
2 minor wind traitstones * 3
2 minor fire traitstones * 6
2 minor nature traitstones * 6
2 minor magic traitstones * 2
3 celestials traitstones * 2
So far: 3 vault keys from 312 drops.
If we multiply the approximate odds of getting a gnome (1 in 30) by the known estimated odds of a gnome dropping a vault key (0.96 in 100), you will have a 0.00032 chance of getting a vault key per match played, or approximately 1 in 3,125 matches. Since 1% seems like the more likely accurate odds of getting a vault key drop (.96 is based off of only 312 data points) I think it is safer to assume that the odds are really 1 in 100 and not .96 in 100, meaning the odds are closer to 1 in 3,000. Keep in mind the odds are probably slightly worse than 1 in 30 to get a Treasure Gnome based on the vague "about 1 in 30" odds given by the developers, however, so the actual odds are probably even worse than this.
If you are lucky enough for a Treasure Gnome to appear, you kill it before it escapes, you win the match, AND it happens to drop a vault key, you can finally earn this achievement. I highly suggest playing the vault battle on easy difficulty - Remember, higher difficulties do not increase gnome rewards.
Monthly, Gems of War will be featuring a "Vault Event" which will make the odds of Treasure Gnome far more likely to appear. Additionally, Vault Keys are more likely to drop during Vault Events. The extremely limited amount of time Gnomes had the increased drop rate immediately after release of the new patch is likely the only reason I and a few other players have this achievement right now.
Every 3 weeks Gems of War will feature a "Raid Boss" event. You must be in a guild for this. If your guild does enough damage to close Portal 5, one of the rewards will be a vault key. This is a very easy way of getting a vault key if you are in a semi decent guild.
I will note that the treasure gnome will take on the rarity of the troop it replaces, so it could appear as a common, rare, ultra rare, etc.
Finally, I want to add that you will not receive the gnome rewards if you manage to kill a gnome but end up ultimately losing the match. You must win the match in order to receive random gnome loot.
Video of the tail end of my Vault Battle: