(edited for better reading) You need to buy 2 tools: wirecutter for the trap floors' box and wrench to reach trap box.
Sorry for the dark screens, the PS4's screenshot ability is poor.
You need 1 rope arrow.
Secret explorer: http://i.imgur.com/5ygwQDp.jpg
Save 8 or 9 Water Arrows for the light cameras. There are 8 or 9 (1 outside which can easily be skipped and 8 inside, not all of which need hit, but it makes things easier)
(you need find all the docs for Big Vault)
1st Doc: 682
2nd Doc: changed second dial from 8 to 3
Big vault combination: 632
Final: Be careful of light camera inside the vault because it sets off a poison bomb in the vault only.. I recommend using a water arrow shoot it.
DON'T TAKE the Necklace after opening last door, instead check table's left side for button to turn off poison trap. (Necklace with two gold cups).
How to get the 2 aerial takedowns on Master difficulty:
It is not easy, but possible - the one I find easier is at the East window-entrace - while leaving the building position yourself facing the window, do not lean because the guard will see you, so just follow the light on the wall. When he starts leaving after staring at the bench start a jump (not a running jump, just a regular one) and while jumping in the window frame you'll get the option to perform the aerial. This is mostly about timing and probably you'll get it after couple of times. What I noticed is that while entering the bank... I just could not get it right, when leaving it works fine... Maybe it's just me, I don't know.
The second aerial is a bit more difficult - this you can only get while leaving the bank for sure. Crouch on the pipe outside the West window entrace at the top floor and observe the patrol down below. Face the arch exiting this area and position yourself a bit North from the line of the crate on your right. When the guard starts to leave, swoop as if you were trying to following him and you will get the option to perform the takefown for a short time. It is important that you swoop almost parallel with the pipe and it has to be a swoop (i.e. forward + jump) and not a jump or a safety drop or it will not work. It will show the takedown possibility but the game simply not accept it. My theory is that swooping brings Garrett close enough vertically to the guard meanwhile still being on a solid surface... because while he is in the air this command simply does not work (i.e. from hanging on a rope arrow or flying mid-air).