Is it "autoshifting" (or "ghost shifting" by you're "won't stay in gear" comment) or does it just shift very poorly when you mean to shift? You don't necessarily have to shift rings first. It all depends on what rear cog you're in when you approach the hill. You may need to shift the rear to get to a part of the cassette that will make shifting the rings easier. Then, shift the rear again until you get to the gear you want. Always shift BEFORE it gets really difficult to pedal, because you will have cleaner shifts when you're not putting a ton of force on the pedals. You can even think about soft-pedaling for a revolution as you shift to ease up on the chain slightly.