For anyone searching around; beware minor spoilers here. I'll be vague to avoid ruining it if possible.
NOTE: Make sure once you finish the puzzles to LOOT the boxes on the staute for it to count. It's not enough to just complete the room puzzles.
1st as part of the story, light the torch the statue is looking at among the many in the room.
2nd when you get to
there will be explosive barrels hiding a mirror just after you enter, blow them up and go through. If you struggle with this, try the anchor discharge next to them and they should explode. NOTE:
*** Spoiler - click to reveal ***This may require the constant focus buildup for the anchor that you get in the course of the story. When your focus meter is a third full you can release it in an explosion that should take out the barrels
3rd is in the library, press the wolf button and go back to the previous area to find the ring of sconces now lit
4th is in the supply tower, just before going into the big door locked with a wheel turning puzzle. Light the bottom floor, then the top floor hallah, then the bird of prey, then return to the basement for the reward
Hope that helps!