So you did your first Mud Run and you finished. But you ranked 874th out of 1000 or not where you wanted. You want to do better. Using the 80/20 principle, here is the core of what I believe will net you the best results without quitting your day job:
1) Get used to running.
Your times will significantly improve when you can get from one obstacle to another...faster.
2) Get used to running AFTER you lift something heavy.
Generally speaking, runnning the day after or even immediately after your weight training sessions are considered counter-productive. This is because people generally lift weights to get stronger and running after is furthering your body's ability to recover for the next strength session. But, obstacle course racing specifically tests your ability to keep running after lifting per se...an atlas stone. It sucks, but get used to it.BUT be careful, as lifting heavy things when your tired increases your risk of using bad form and hurting yourself.
3) Practice running/walking up hills.
This separates the men from the boys or the women from the girls. It usually will determine whether your in the top 10% or the bottom 10%. I feel like this is more technique than it is conditioning, although both are important.