(Note: all life upgrades are in the past)
Near the bottom of the main fortress entrance stairs (in the past) there's a raised area with another staircase on it. When facing the staircase and standing at the bottom, there will be some barrels to the left. Smash the barrels to reveal a switch. This switch opens the rat-trap gate at the top of the stairs. It will close before you can get to it. It is possible to reach it by jumping over the stair railing, and wall running on the left side as you go up the stairs, but it's much easier to just come back after you get Eye of the Storm. You won't really need extra health before then, anyway.
There is a large stone object in the center of the upper platform, just up from where you fight Shadee the second time. Grab it and pull it toward the stairs and the wall will open. Try to get this as soon as possible. Coming back to this area at the end of the game can causing game-stopping glitches.
Turn the switch in the central hall so the gap in the floor is filled. On the west side of the walkway, there is a place where you can drop off the edge, then wall jump to a lower area. Run along the wall, then jump near the end and wall jump up the top of that structure, and then run on the next wall and wall jump down until you're hanging on the ledge. You should be able to jump across and shimmy around to the platform. The life upgrade is through the door.
There is a gap in the railing in the room with all the trees. Jump through it and you can shimmy along a ledge, then run across the wall to get to a tunnel that contains the upgrade. Get this as soon as you can as it gets sealed off late in the game.
Water switch room
Wall-run up to the ledge in the room that contains the switch you use to turn on the water.
In the big room where you fight the third golem and activate the clock tower, there are several breakable walls. When standing in the entrance and facing the golem, there is a switch and save fountain on your right and a life upgrade on you left. Stand in front of the wall, and then wait for the golem to throw explosives at you. Alternatively, you could come back after getting the scorpion sword and break the wall yourself.
In the room above where you get the scorpion sword, there are two breakable walls. Break them both, activate the switch in one, then use Eye of the Storm and run tot the other. You only go through this area twice and you can't come back, so be sure get it when you can.
When you're walking on the big donut-rings above the library, you can jump to some ledges in the wall from the second ring. Shimmy to your right to reach the door to the upgrade. You must get this your first time through as the ledge become impassible later.
There is a breakable gate on one of the platforms on the top floor of the antechamber in the southern passage. After you get the Scorpion Sword, come back, break the gate and drag the block out onto the platform. You can use it to wall-run to an area above the platform where you can find the final upgrade.