Life Upgrade #1: (PAST) After fighting the girl in black a second time, pull the large altar on ground level of the sacrificial chamber to reveal a secret door. Go through the trapped hallway and bag the first life upgrade.
Life Upgrade #2: (PAST) This is after Slow Time is earned. From the room where the Prince has a cut-scene with the maggot man creature, head back out into the large courtyard like room with a timed floor switch next to some stairs that opens a low gate at the top of the same set of stairs. Go through that trapped hallway for the second life upgrade.
Life Upgrade #3: (PAST) This is after the Serpent Sword is earned. Rotate the turnstile switch directly opposite the facing of the metal nub the Serpent Sword was used to create platforms to a door at the bottom of the chasm. Use long wall jumping to slow the Prince's descent down to the level of the door. Past that door is a trapped hallway that leads to life upgrade #3.
Life Upgrade #4: (PAST) When exploring the Garden Tower, look for a room that is overgrown with vegatation and is right below a box and folding bridge puzzle (it is in the same vicinity as the first switch that turns on the water for the Garden Tower). A break in the fencing allows the Prince to drop off and use ledges to access a door underneath the overgrown vegetation room. The fourth life upgrade is past that trapped hallway.
Life Upgrade #5: (PAST) When exploring the Clock Tower, look the giant golem enemy that throws explosives. One breakable wall is a save point, but there is a second breakable wall on the other end of the room leading to the life upgrade.
Life Upgrade #6: (PAST) After gaining the Scorpion Sword and a particularly tough giant golem encounter, a ladder leads the Prince to a Roman courtyard room; two breakable walls are here -- one has a switch, the other has the door which requires slow time to access. The life upgrade is past that door