Why keep that Air 2 on 8.1.3? Battery for iOS 8 went as follows in my personal opinion: 8.2>8.3>8.1.3 and below. Some people thought 8.3 was even better than 8.2, some had similar results to me with 8.2 being the best. Either way, 8.3 will probably be better than 8.1.3. On my iPhone, 8.1.3 and below was the most dreadful for battery life. I struggled to get 4 hours of use. 8.2 typically was 8.5 hours or more, which is good for iPhone. 8.3, I get 7.5 or so.
Pretty much before 8.2, all my devices were absolutely spammed by jetsam events, stacks, stacks+backboardd, and backboardd logs. I got to a point where I got nearly 30 stacks+backboardd logs a day. Restored as new and it didn't help that much.
8.3 should be at the very least the same battery life as 8.1.3. If it isn't, try iOS 9. You can still downgrade at this point if it doesn't do well. I've heard nothing but huge battery life issues on iOS 9, so it's at your own risk.