It appears that your Android SDK install is incomplete/corrupt/mis-matched.
If you run the Android SDK manager (or Android Studio), are any errors reported? Use the manager to update to SDK 24.3+
If you still have problems, post the entire log as a gist.github.com (or similar) so we can have a look at the entire trace from XS.
Also are you on Windows or OS-X?
Xamarin Studio
Version 5.9.4 (build 5)
Installation UUID: c9eca622-356f-4681-a1d2-069016cc404f
Runtime:
Mono 4.0.2 ((detached/198235d)
GTK+ 2.24.23 (Raleigh theme)
Package version: 400020004
Xamarin.Android
Version: 5.1.4.8
Android SDK: /Users/administrator/Library/Developer/Xamarin/android-sdk-mac_x86
Supported Android versions:
2.3 (API level 10)
4.0.3 (API level 15)
4.4 (API level 19)
Java SDK: /usr
java version "1.7.0_45"
Java(TM) SE Runtime Environment (build 1.7.0_45-b18)
Java HotSpot(TM) 64-Bit Server VM (build 24.45-b08, mixed mode)