Running upright and relaxed is the best running position. Your head, shoulders and hips should be over your feet, making it easier to move your whole body, and improves your breathing. Strong ab muscles will help maintain form; sit-ups and planks can help improve core muscles.
Hold your shoulders back and relax your body. Imagine a string attached to the centre of your chest, leading you up the hill. Shift your hips forward to keep your alignment and posture correct.
Leading with your knees will keep your alignment correct and prevent over-striding. Pushing off from the ankle with short fast steps is the proper motion; it should feel like a shuffle.
Breathing can increase speed and efficiency. As your pace increases it is common to take shorter breaths, similar to gasping. Breathing should come from deep in the belly, not from the upper chest. Focus on exhaling; the inhale will happen on its own. Over time, breathing will feel more natural and comfortable.