This achievement requires you to earn an "Epic" vault key from a treasure gnome, and then use that key for an epic vault battle, and win that battle. Unfortunately, this is likely going to take a large number of battles in order to achieve based on the math below.
Treasure gnomes appear randomly in battles, replacing one of the normal troops. Treasure gnomes can't replace troops in event battles, so stick with explore or (non-faction event) delves.
When you defeat a gnome, it has a chance of dropping various loot. One thing that it can drop is an Epic vault key, but the odds are very low.
Every so often, a "Gnome Vault" event pops up. This is your best opportunity to get this achievement, but it will still take a large number of battles.
During a gnome vault event, the odds of a gnome appearing are significantly increased. Here is a thread that discusses the likelihood of gnomes appearing, and their odds of dropping an epic vault key during gnome vault events only
According to that thread, gnomes will appear about every 10 battles, and it takes on average between 12 and 15 gnomes before you will get a vault key. On average, between 10% and 12% of vault keys will be epic vault keys. Based on two different vault event weekend data collections, that thread determined it will take, on average, just over 1,300 battles
to get a single epic vault key, and that's even during the event weekend. The odds would be much lower outside of a gnome vault event, to the point I would not go for this achievement outside of a gnome vault event.
Once you finally have your key, you are still going to need to win the battle. While your rewards will be worse, it is worth considering playing at a lower difficulty to better ensure victory, but that gamble is up to you.