Every character will unlock 2 levels of their bursts by reaching a certain level, but level 3 requires quests of sorts to unlock, here are each of them.Found from traversing from the tutorial to Harm's way, just after Garrison joins your party.
Armaments of Legend (4) All are found at Pale Cathedral.Studies of the Arcane: Time Warp (3) Related to Knolan's level 3 burst, more details under that section of achievements.From here head down/to the left and then at the next fork take a left through the thorny area once again, when you exit head down just a bit and on a sole hedge there will be a lamp post, and to the right of the post will be your last Lore - An Endless Maze - Arrival (4/4). Keep heading up and at the next fork head left and in a corner you'll find Lore - An Endless Maze - The Chaos Underneath (3/4). Head to the right gate and then go down, take the last intersection heading up and if you hug the left wall about halfway up you'll find Lore - An Endless Maze - The Eyes of Everything (2/4). From here, backtrack to the intersection and head back down, then to the right at the next fork which will lead you back to the starting square with the statue. At the first fork this time head up/to the right then at the intersection, head left and you'll come to a pile of bones to find Lore - An Endless Maze - Moonlit Shadow (1/4). Talk to the statue to start the maze and head through the left gate and head left.An Endless Maze (4) All are found at The Winding.