Yun did not design for battery operate and has no PMICs .
TPlink TL-MR10U which has same CPU AR9331 as Yun, with 2600 mAh 18650 battery, will last 7-8 hours.
The heart of PMICs (Power Management ICs ) is LTC4088 - High Efficiency Battery Charger/USB Power Manager.
TPlink TL-MR10U come with 32MiB Ram and 4MiB Flash, I have it hardware mod to 64MiB/16MiB (same as Yun) and connect MCU to UART port of TL-MR10U. We are in the business.