The minigame is the game right in the menu. You use WASD to move and Q to launch grenades. Don't bother with the gun, it is inefficient.

Move to the center and start lobbing grenades at approaching zombies, try and maintain a perimeter around your character. You can lob grenades in front of zombies and they almost act as a trap for them, as they will spin for a few seconds before firing. This technique requires alot of clicking (hit Q as fast as you can since you cannot use the keyboard repeat function from what I can tell).

Doing this for a set period of time, about 90-100 minutes will net you all of the kill menu zoms achievements and the madness / survival achievments. You get the timed ones at 15, 30, and 60 minutes, and kill number achievements at 50,100, 500, 1000, and 5000. You need to get the 5000 in one life, according to the developers' comments in the Community Hub, so take care of any bio needs, get comfortable, and prepare to click away for 90-100 minutes, and get 7 achievements.

If you played PP: Japan, this will be familiar.

You get one achievement per puzzle, and one achievement for completion of each layer/column of the sideways pyramid. There are 19 puzzles, and 5 levels, for 24 achievements. I recommend solving the puzzles for the achievements without zombies, initially, or at least do the first one if you are unfamiliar with the interface. It is obviously much easier to get the achievements without worrying about your guy being killed, but it is your game to decide how you want to play it, right?

The last three achievements are for the zombie survival phase of the game, and can be completed in one go, and I recommend the first puzzle for simplicity.

You need to assemble enough pieces to get points for claymores and grenades. You have a barricade at the end of your 'base' which is all you need or want.

Move down to the lane where the zombies will come down, at the bottom of the screen. Start assembling pieces until you can get your first claymore, and set it all the way to the left. [ ] at the bottom. Continue to assemble until a zombie hits the claymore. Set another in the same spot and another a few squares to the right. Do this until you are able to set 5 claymores total.

IF a zombie comes before your ready with claymores, no worries, just throw a grenade (Q) if you can, or shoot the gun with (space). Grenades are preferred because they one hit kill and get you closer to the nade thrower achievement. You should grenade them 3 times total, as 3 grenades and 5 claymores gets you the Nade Thrower and Claymore achievements. Then, just let the zombies tear down your barricade and kill your guy. This gets you the Chomp Chomp achievement.

As I said this is a simple guide; I realize I should add screenshots, and I may, should it be needed.