I've been a GM for about three years now. I've been GMing for this group for almost two years next month. I have an issue with motivating my players to take action.
It's a sandbox campaign and they're currently going after the BBEG's old lairs to get clues on who he is and how he was defeated before so they can defeat him. The players have somehow got it in their heads that the BBEG is out to kill them; this is not the case because if it was the BBEG would just kill them and there wouldn't really be anything they could do about it, hence the fact that they're searching old lairs for ways to defeat him.
So I have tried laying out side quests where they get to be heroes, which is something the group has told me they wanted to be, to help them power up and gain experience, they even have mythic ranks. However whenever I present something to them that isn't just a straight up monster hunt or a murder mystery, they go "No way are we getting involved, it isn't our problem." The only way I've managed to get them to do anything heroic so far is to use the paladin's code to get the paladin to try and help people and save lives. On top of that I create villains and bad guys for the party to go up against, setting them up for awesome fights, and they retreat thinking its too dangerous, and once again, it isn't their problem.
I have tried using money to pay them, I have tried using their character motivations, but they seem dead set on ignoring everything in the world outside of the "main quest", in a sandbox campaign due to something that has not come up once since its introduction and there has been no in game reinforcement of.
If it helps, the party is level 5 mythic rank 2.
TL;DR: What method can I employ to get my heroic minded, but not heroically inclined, group of players to explore more of the side content so they don't get wrecked at the fight with the BBEG?