Guiding the spirits
While exploring you may come across a mysterious spirit - you can't catch it, can't attack, but you should follow it.
The first few you find will just lead you to a statue, and once they touch that statue, they will unlock a chest as if from no where. You really can't complain about that.
But more than that, you may eventually find an area with multiple statues. All of the spirits nearby will be necessary to unlock your reward, and they won't be too far away. Generally follow the direction the statues point in, and you should be able to see nearby spirits pretty quickly.
Occasionally you will see several round enemies just floating in the air. Yep, this is target practice, and you will want to shoot them down.
Of course you get Amber very early on in the game, and she's a great (low-tier) party member if you're in need of a Pyro, but more important than that is the fact that she uses a bow and arrow weaponset.
This is important as these challenges can only be completed with a bow, and even those mages which shoot long-distance magic attacks can't be used in order to clear this. Once all of the round floating enemies are shot down, a chest will appear nearby.
Combat and gliding challenges
You will sometimes come to a small obelisk which, when touched, will propose a challenge to you, and yes, it's a crying shame that these obelisks don't tell you what kind of challenge you're getting into until it begins. Nevertheless…
Sometimes you'll be tasked with defeating a group of enemies, which is best done with whatever element they're weak against. These tasks are only really tough because you will often be timed, and must defeat the enemies within a strict time limit.
What's much more fun are the gliding challenges, which are reminiscent of the glider license challenges you undertook with Amber near the beginning of the game. Just sail through all of the rings and you'll quickly find a chest at the end.
Three tiny windy boys
The three tiny windy boys will often lead to Anemoculus or Geoculus, which are the items you offer up to Statues of the Seven in order to receive rewards and permanent stamina upgrades.
You'll see them on the ground, small white wisps, and when you walk through them you'll have a wisp follow you. Now walk through at least two more, which should be in the nearby area.
The final wisp will transform into a gust of wind shooting upwards, and this will allow you to glide and either grab a floating Anemoculus or Geoculus in the air, or float down safely onto a chest which is surrounded by a barrier. Once the chest is open, the barrier will disappear.