There are 6 life upgrades...if you take them it will be much easier to play the game knowing you still have some health...so here there are:
1: After you have finished playing as the dark prince for the first time and are the prince once again climb until you are near two doorways. One should have saw blades going around the corridor and a save fountain down a little ways. Don't go down this way. Go through the other corridor and continue jumping until you reach the fountain.
2: There is a large room right before the 1st boss. (The big guy with the sword.) Once you activate the dagger switch two doors will begin to open. The upgrade is in the door that is the farthest away from the lever. Go down that ramp and roll under the door before it closes. Continue down til you reach the fountain.
3. After you see the vizier cut down one of Babylon's guard you will become the dark prince. After you reach the room where you see the vizier leave you will once again become the normal prince. This is the room where the upgrade is. Turn the lever to drain the water and climb up the pole. Run along a wall till you are on the swinging poles and you should see a hole in the wall covered by a curtain. Make your way into that and continue to the fountain.
4: After you destroy the stone guardian. (The boss you ride on.) You run up a wall and there is a save fountain. Instead go right and roll through the hole. Continue to the fountain.
5: This one is in the elevator room. After climbing up for a ways there should be a lever that when turned will open the door right in front of you. Do not go in that door yet. Instead you should see some dagger plants on the elevator shaft. Climb up those then wall jump to the pressure pad. Slow down time then get back down and go through the door that opens. Continue to the fountain.
6: This is while you are climbing the palace. This is a little difficult to spot. Once you are climbing the palace for the first time and then going back inside to the trap filled corridor and once again back outside (after a save fountain) this is the area of the upgrade. After the fountain there is a dagger switch that opens a door. There should be enemies outside of it. After climbing a little ways you are at the second lift (with the box). Right before you go back into the tower there is a platform where you will be prompted to use the landscape view. This will show a way to get down to the area below. Following this you will make your way to the fountain.