I understand this is an old post, but I also had the same issues updating from the ADB recovery screen with any of the firmware updates listed, and even the newest (KitKat) one UL-K010-WW-2_2_33_144-user.zip. The solution was to apply the signed version with the tablet booted into droidboot. The signed zip has images for all of the partitions, whereas the official firmware is missing recovery.img and system.img.
Post #215 from
[Q] Asus Transformer Pad TF103C Tablet - Roo… - Pg. 22 | Android Development and Hacking has the link for WW_TF103C-2.2.33.144-release-user-20150827-signed.zip
From here you just boot into droidboot (unplug tablet from USB, hold volume up + Power for 3 seconds until the screen turns on), then plug the tablet into your computer over USB. In Windows, extract the -signed.zip and open a command prompt (cmd.exe), change to the directory where you extracted the files. From the command prompt, run:
flashall_AFT.cmd 1
and it will update all your partitions. Once completed, the tablet should reboot & you will be on the latest KitKat version. From there, you can download the Lollipop upgrade UL-K010-WW-12.10.5.11-user.zip from the official Asus firmware page, extract the .zip file inside & place it either on the internal /media/device/ (over adb), or on an external SD in the root folder. After a reboot or two the device should detect the upgrade which you will see in your notification bar. You can then select it from notifications & the upgrade will commence.
Good luck!