Ziggurat 2

Gauntlet is a mission type available during campaign. It shows up in the earlier chapters (I noticed by first on chapter 4 so can't confirm if it can be earlier) and pits you against 15 waves enemies per mission length, playing out much like the challenge chests (chests in rooms with the battle axe symbol)

To play through 60 waves, you need to get a gauntlet mission with a length (those moon like symbols) of at least 3.
You fight 15 waves then get a break with a chest or a shop. After the 4th set, the achievement is yours. I was afraid I'd need to find a way to have 1-60 show up at once like some sort of survival test but no, just the 4 sets of 15 and you are golden.

Happy hunting (>*_*)>