The other thing I did today was I maxed out my team on the Raid Boss event before using anymore sigils up on battles. I did that because the fights get steadily harder and I was getting into territory where the fights were challenging.
A quick and dirty run down:
You need to complete the first ten battles before you can collect Rewards. Even if your team is racking up loot, you can't get to it until you've completed the first four stages, which is a total of ten battles.
It's generally a good idea to buy up to the event weapon at Tier III and to use whatever boss slaying troop is available, which seems to usually be a new troop introduced that week. You can get copies of it from the Raid Boss Shop and, I think, sometimes Event Keys or Glory purchases.