There's a pretty good video tutorial here:
.
This video describes an 8.4.1 downgrade but the process is the same for 6.1.3. IPSW files can be found here:
https://ipsw.me/#!/platform - remember to select the appropriate iPad 2 model (Wi-Fi, GSM/AT&T or CDMA/Verizon).
If you're a Windows user, I'd use Beehind instead of OdysseusOTA. It's basically a slick GUI wrapper for Odysseus which means you won't have to bother with terminal commands. Just remember to run it as administrator (right click->run as admin). I also believe you need to download java first if you don't already have it on your PC. Tutorial:
Before you begin with either of the above methods, you need to jailbreak your device with Phoenix (I assume you're running 9.3.5, otherwise update to 9.3.5 or download the appropriate jailbreak tool for your firmware). Tutorial found here:
http://www.idownloadblog.com/2017/08/10/jailbreak-ios-935-phoenix-move-from-version-1/
When your device is jailbroken, you also need to install OpenSSH. Simply open Cydia and search for OpenSSH and install it.
Let me know if you run into any problems. I've performed the process on an iPhone 4S using both OS X and Windows.
[doublepost=1514985164][/doublepost]Another way to get an older iOS version running on your device is to dual-boot two iOS versions using CoolBooter. Start off by jailbreaking your device, then download CoolBooter through Cydia (first add the coolbooter.com repo). This tool will allow you to partition the device's internal storage and let you switch between the current firmware (9.3.5) an an older firmware of your choice, such as iOS 7 or iOS 6. I think you can even go as far down as 5.0 with CoolBooter. The downside of dual-booting is that you won't be able to use the full storage capacity on either OS since the internal storage will be partitioned - so, unless you're craving for iOS 7 or iOS 5, I'd recommend using the OdysseusOTA/Beehind approach. I played around with this for a bit on my old iPhone 4 (dual-booted 7.1 and 6.0) and it seemed to work okay.