Life Upgrades can be found at the following locations:
1 (Past) After you fight 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 get the first Life Upgrade.
2 (Past) This is done after Slow Time is earned. From the room where the Prince has an intermission sequence with the maggot man creature, go into the big courtyard-like room with a timed floor switch next to some stairs. This switch opens a low gate at the top of the same set of stairs. Go through that trapped hallway for the second Life Upgrade.
-Note: To acquire the second Life Upgrade without getting the power that slows time, you must find the switch behind the barrels. Press the switch and wall ride up the wall, instead of running up the stairs roll. If done correctly, you should make it a moment before the door closes.
-Note: Use the following trick to get the second Life Upgrade early on When you first travel into the past after the intermission sequence of the Prince following the girl in black and she kicks you in the face and runs off, go back out of the hallways as usual. However, retrace your step leading up to this (the first fight with the crow Boss). Run up the wall then get up on the ledge. Wall run up the second wall as before. Now everything is intact. You should reach a set of stairs. There are three barrels on the right-hand side of the staircase that hides a pressure switch. Walk onto the switch then run to the side of the staircase. The Prince will hop the railing and start to roll up the stairs. As soon as you can, roll all the way up them to a small hole in the wall at the top. Once inside there are several set of spike traps, rock pillars, and timed swinging swords. Make your way to the end of this hall to get the very first Life Upgrade and deactivate all the traps. Run back to the hole you rolled through and there is a another pressure switch on your left. Wall run to press this switch and open the hole. Roll back out then make your way back down the hallway below and the fountain to save.
3 (Past) This is done after the Serpent Sword is obtained. Rotate the turnstile switch directly opposite the facing of the metal nub where 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 the third Life Upgrade.
4 (Past) While exploring the Garden Tower, look for a room that is overgrown with vegetation and is directly below a box and folding bridge puzzle. It is in the same area 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.
5 (Past) While exploring the Garden Tower's second water puzzle, ledge up after turning on the water (but before exiting the room with the turn switch) for the fifth Life Upgrade.
6 (Past) When exploring the Clock Tower, look for 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 leads to the sixth Life Upgrade.
7 (Past) After obtaining 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, and the other has the door which requires Slow Time to access. The seventh Life Upgrade is past that door.
8 (Past) After you enter the Library, the Prince will need to pull out two bookcases to continue his progress. Look for two circular ledge/beam structures (one of which will have a Ninja) after dealing with the bookcases. One of the circular ledge/beam structures leads to a wall with three levels of ledges that may be climbed/sidled. This is a detour to the eighth Life Upgrade.
9 (Past) There is a location near the start where you chased Shadee (girl in black) and a door shut behind her. You then have to go up a set of platforms to finally reach the switch atop the room, just before sacrificial pit. Go back there when you get a sword that can break walls. Make your way back up this room. Look carefully when on the top platforms. There should be a set of metal bars in one of the wall that seem damaged. There is a crate behind those bars. Break the metal bars with your sword. Bring the crate onto the platform and look up. You can use the crate to access a passage in the roof to reach the ninth Life Upgrade.