Arduino Yún and battery life
The amount of power your entire system will draw is highly dependant on what your circuit actually does, but if you're only going to be using a few small sensors and the majority of your power draw is from the Arduino Yun we can make some estimates. 

Adafruit has an excellent comparison of embedded linux boards, including the Arduino Yun, and details the current draw: here. 

With WiFi ON the Yun draws approximately 280mA at 5V. (Note: The Arduino Yun does not have a voltage regulator on board. You would need to make an external voltage regulator for your chosen battery to ensure the voltage stayed at 5V - else you could fry your board.) 

Using $$P=IV$$

We can calculate the power draw to be about 1.4W. 

Let's assume you use a regulated 5V lithium battery, something like this (not cheap, but high capacity and regulated!) 

The battery is rated at 27Whr - which means it can provide 27W for 1 hour. 
If we're consuming 1.4W we can expect the battery to last: $$\frac{27}{1.4}=19.2hr$$ 

So even with a high capacity battery you're only going to be able to power your controller for at most a day. Hence, battery power probably isn't the way to go and isn't practical. 

Try a 5V DC power pack which you can plug into the wall.