One of the worst possible injuries you could get as a runner would be a rupture of the Achilles tendon.  

Because if you tear the Achilles, whether you have surgery to repair the Achilles tendon or you if don't have surgery and allow the tendon to heal without surgery, even if it heals, I can promise you, you are never going to be the same.

Running hills puts a lot of stress on the Achilles.

If you have Achilles tendinitis, Achilles tendonosis or just mild Achilles irritation, understanding what to do to avoid rupturing the Achilles will also help you avoid aggravating the tendon when running hills. 

There are really three simple things that you really need to do when you're going to run up hills so that you don't put yourself at risk of an Achilles tendon rupture.