Call of Duty: Black Ops II

This can be done solo on Easy difficulty.
An easy spot to hold out is right at the PDW-57 below the spawn which happens to be beside the Quick Revive elevator. You can get there by buying the spawn door, then clearing the debris for the escalator. Alternatively you can take the elevator down to the floor by hopping onto it if you want to save some points (this applies only in Solo mode).
Either way you will see the gun on the wall beside the elevator shaft on the floor below the spawn. Be sure to pick up Quick Revive if you're playing solo, which becomes available to you whenever the perk machine drops down/comes up to that floor (in co-op this elevator shaft stays powered off). Buy the PDW and hold by the window where you can see the Dragon. Watch the barricade by the elevator to the left and aim at the head! Buy more ammo when you need it (only 500 points). The only hard part is when the Minion wave comes. A helpful tip to deal with these guys is to make sure that you have Target Assist turned on in your Options menu. If you Aim with repeatedly with this option turned on you'll keep 'snapping' to your targets so you'll miss less shots. Watch the video below for an explanation on this trick.
As soon as round 10 starts, the achievement will unlock.
Your best alternative is at the Mystery Box in the upside-down skyscraper. Another alternative is by the AK-74u, but that one is more dangerous since zombies can hop up on the overlook where the gun is.

*Final update to this solution Apr 15 2017.

Collect the pieces to build the Trample Steam, and every player needs to take one of all four. Just make sure each player takes one, and jump two floors above you. There is a gap right next to the escalator.

If you made it, then just start building the artifact. Each player must put their part. After it is done, take it and you could either put it in front of the dragon, or facing the other building next to the Quick Revive elevator. On this video I jumped to the other building. If you are going this way, make sure the other player you are going with, has an available Trample Steam, if not, you are not going to be able to jump to the other building. So, set the Trample Steam facing the building and then just get on it. Once there, start opening doors until you get to the roof, where you will survive until the tenth round. Remember that the MP5 is right there and you can buy it whenever you want.

Another good location to do this at would be near the power room by the 870 if you're playing with more than one person. I did it with two others while trying to find parts and its relatively easy since nearby you can build the new wonder weapon. stay near the elevator and everyone can watch a side, although it seems most zombies come from the doors and hallways and not the elevator or window.

Probably one of the easiest No power achievements in the zombies series, just go the opposite way of power, by the mystery box and into the upside down building, its easy to camp there for at least 4 rounds, the room i stayed in had only one other entrance so we could also get the tramplesteam achievement.

Black Ops 2 Zombies Mad Without Power Achievement Guide/Trophy

You need to get to level 10 without turning on the power. This guide will show you how