When you're monkeying around on the hanging cages in the Prison area, you might notice some blue flecks in the air. See that suspicious-looking alcove at the upper right? That's where they're coming from, but you won't be able to get there for a little while. So for now, continue as normal and get ready for a fight once you reach the ground floor.
After the fight's over and the puzzles are solved, you'll be able to use two freezable waterspouts and the wall to reach this beam:
Go ahead and trigger the nearby switch, and then run down the trap-filled hallway and through to the slowly closing gate.
As soon as you're clear of the gate look to your right and you'll see a bunch of loose bricks. Dash on up there.
Another dash or two, and you'll be hanging from this ledge, where your next course of action should be obvious: wall-run over to the next ledge, then wall-run to the horizontal pole.
This will trip a switch that opens the gate in front of the Sarcophagus. From here, all you have to do is swing over to the next pole...
... and Sarcophagus 4 is as good as demolished.
Shortly after entering The Sewer, you'll come across this room, where you'll have to freeze and climb the vertical waterspouts in order to get up that ramp on the far side of the room. Climb the first one, and then hop onto that horizontal beam.
From here, freeze the water and start climbing it as soon as it starts flowing heavily, but don't jump to the next spout just yet.
Instead, just keep climbing...
... and near the top, you'll be able to swing the camera around behind you to see the next Sarcophagus waiting.
Jump backward onto the nearby beam, and the next Sarcophagus will be just a short hop away.
For the sake of easy reference, we'll start this one in the room where you have to turn a crank in order to rotate the two big waterspouts, which you'll then use to climb to the next area.
Continue across the spike-filled pits ahead as you normally would.
Around the corner, you'll encounter a fork in the road, with more of those blue flecks milling around. To the right is the path through the rest of the level, so you'll want to go straight instead.
Run out across the beam next to the fork, and the camera will pan around to reveal your next target.
This next bit is a little tricky, but it's a good chance to practice a skill you'll have to rely on heavily later in the game. When the first spout activates, wait a second, then freeze it and jump on.
The second you jump off it, release the freeze button. If you've timed it right, the next spout should activate before you reach it. Freeze it, and the next Sarcophagus is within easy swinging distance.
It's pretty easy to see this Sarcophagus' hiding place, which is in the room where you'll be introduced to a horde of sand monsters with this cheery camera angle:
Above: That speck at the top of the banner is the Prince sliding into danger
Once you've dealt with the fiends, look around and you'll see this waterspout - flanked by two conspicuous switches and a locked door - at the far end of the room
Climb the frozen waterspout and jump off to hit one of the switches before immediately jumping back from the wall.
Above: You can run up the wall to hit it if you need to
As soon as you're back on the spout, IMMEDIATELY jump over and hit the other switch the same way. If you're quick enough, the door will open.
From there, all you need to do is climb back up the spout and jump into the secret room, and you can smash another relic to pieces.
After you've spent another exhilirating segment in Ratash's line of fire, you'll reach a room with a fountain, a couple of waterfalls and a high, domed ceiling. It looks like this:
You'll have to climb to the area above anyway, but that doesn't mean you'll spot the Sarcophagus immediately. So for starters, freeze the waterfall and the spouts, and use them to run/swing up the shaft.
Once you're at the top, though, you might notice that oddly shelf-like ledge at the top of the right waterfall. So bounce off the water and grab that spout...
And then turn around to face the direction you came in as soon as you grab it.
Now, leap off the frozen spout and release your Flow power to unfreeze the water.
Assuming you nail the jump, you should find yourself on the ledge, just behind the waterfall and within easy reach of the next Sarcophagus.
At the end of the Royal Chambers area, just before you reach the massive Observatory, you'll see this big waterwheel.
Climb up to that first ledge, but resist the temptation to just freeze the water and dash across. Yes, it's how you'll get to the next area, but there's something else you need to do first.
Instead of dashing left, dash straight up and you'll find a bunch of convenient handholds - and blue flecks.
Jump off from the top of the bricks, grab hold of the horizontal pole and leap onto the ledge on the opposite wall. From there, all you need to do is drop down and the next Sarcophagus will be yours.
Next page: The Throne Room, The Terrace, The Rooftop Gardens and The Acqueducts