This achievement requires you to survive the mini-game in the menu for 15 minutes. It's not precisely hard, but it is tedious and will start to tire out your hands since you cannot pause or take a break.
If you're going for all of the achievements, you'll get this while trying to get
so should just focus on the 60 minute one.
The following instructions are essentially identical for the above achievements, except for the shorter time interval required.
The basic strategy is to start by using the W, A, S, D keys to move to the center of the screen. After that the only key you'll press is the Q button to throw grenades (don't bother shooting the gun). You will spam the hell out of grenades: you have an unlimited supply, they are instant kills, they can sometimes take out multiple zombies if they're clustered close, and they can also take out zombies that are in close proximity to the grenade when it explodes so your aim doesn't have to be as accurate.
From the center of the screen, use the mouse to control the direction you're facing and just keep throwing grenades. After awhile you'll start to notice a circle/halo of blood surrounding your character. This basically defines the edge of the kill zone and you can use it to judge which zombies are getting closest to you. Preferentially target those inside the circle or closest to it. Undoubtedly a few zombies will get quite close to you over the hour; just patiently aim and take them out at close range.
You have to keep this up for 15 minutes, which isn't too bad (relative to the longer time-interval ones). Your hand(s) will become tired, but there's little else you can do (switch up pressing fingers, quick flexes, etc.). The game does not get more difficult over time; there are some thicker and heavier waves of zombies, but they are just as frequent at the beginning as an hour in and the speed never changes.
If you're going to go for this achievement, there are a number of achievements for the number of zombies killed which you'll get along the way. You'll find that the kill rate is pretty steadily ~50 per minute (or 250 per 5 minutes, 500 per 10 minutes, etc.). Thus getting the 15 minute survival achievement will net you roughly 750 kills and the following:
It will also put you 75% of the way toward achieving:
and 15% of the way toward achieving: