In the folder: obj//android/bin/classes folders exist with the md5sums. If you search the one containing the activity (Activity1 by default) you will have found the md5. You can use it to start and log the App. Then you can do the following.
Install the APK
adb install -r <PathToAPK>
Start The APK
adb shell am start -n <appid>/<md5sum>.Activity1
Log the APK. (stdout: ex. Console.Write) (windows, thru cmd... better for PS)
cmd /C "adb logcat | findstr /i mono"
Log the APK. (stdout: ex. Console.Write) (unix)
adb logcat | grep -i mono