There are many ways to go about this. You will need to engage into a running program that is designed for half marathons. Adding circuit training will help as well (especially those that include body weight exercises, sandbags, ropes, few kettlebells). Also big part of your running should include hills, dirt roads and sand surfaces. When running try to do some exercises every few minutes (maybe every 5-10 minutes do some push-ups, burpees, sit-ups, jump squats, bear crawls, etc.). Below you can find some more information about preparing for an obstacle race:
You can also contact a gym close to you that offers obstacle course training and added to your list. Good luck!