Got my first 15/15 today (3rd day with it open), and it was pretty easy, thanks to tips here. I think I may have gotten lucky once or twice with favorable matchups, but it still felt great to nail that last fight.
Best tips I got from this thread:
1. Replaying battles for optimal result (had no idea I could do that until reading this post).
2. Resetting first thing, before doing dailies and improving heroes. Makes it a lot easier.
And here is one I haven't seen mentioned here, but I think it is useful:
3. Don't buy your Guild hero right away. I was going to grab an extra healer, but decided to wait. I had a tank take a big hit right at the end of fight 13 and was in shoddy shape for the last 2. Bought a Tank instead to have one at full health, and cruised to a victory. So, wait until you know what you need situationally before committing to a Guild Hero.