The screen and Clash of Clans seem to be using half your power all by themselves. But you seem to be getting about 10 hours on a full charge (assuming you drain the battery to 0, which is only okay if you like buying batteries frequently - charging at somewhere around 50% gives the longest battery life), so you're getting about normal charge life. You can probably eke out a few percent more by tweaking the life out of the phone, but all that work for 3 more minutes of battery life hardly seems worth it.
If you need to keep the phone running longer than it does, buy a larger battery (which will make the case larger, since it comes with a deeper back, if you buy anything decently larger, like twice the capacity of the stock battery). Or you can buy a 10,000 mAh external battery that you can plug the phone into when the internal battery starts getting low.
If you can afford to turn the phone off for a few seconds when the battery gets low, you can just carry a couple of spare batteries with you. Two batteries and a charger will run you under $20 and give you 3 times the battery life.