You'll wake up with your new PED suit, which is already equipped with Hyper Mode - many enemies and bosses are only vulnerable to the Hyper Beam. Before you leave the room, be sure to scan all the red logbook entries. Now it's off to the Aurora unit again, where you'll resume your previous mission - seeking out the corrupted unit on Bryyo.
Your first order of business is in the room Gateway. Move towards the door with two dragon-shaped locks on it. The crumbling bridge will hold you long to turn around and notice that a ledge can be pulled with the Grapple Lasso, granting you access to higher points of the room. Before heading to them, however, move to the right of the dragon door and jump onto the towering platform in the middle. A Morph hole leads to a bomb panel that will unlock one of the dragon symbols. One down, one to go.
Head back to the ledge you pulled down. Climb up and you'll see a path to the right and one straight ahead that follows the wall of the Gateway room. Take the wall path (using platforms that activated once you unlocked the dragon) to the top of the tower and you'll see another Morph tunnel that leads to another bomb panel. This one unlocks the second dragon seal, plus moves a small bridge down for easier Gateway access. Head back to the dragon door and take the Morph tunnel to the right, follow the path to Reliquary II and you'll obtain another Energy Tank. Yank the metal grate off the wall and you'll also see a new piece of Lore - collect 'emall!
Back in Gateway, head to the red missile door into Grand Court Path. Along the wall you'll see a statue that contains Fuel Gel - charge blast it and you'll have a stepping stone to reach a missile upgrade in a nearby cranny. Proceed on and you'll see a growth that can only be blown away by the Hyper Beam. Do it, continue on, beat the new enemies that show up and continue outside. Note - this room, Grand Court, will come into play much later in the game. The Ice Door and golem both contain power-ups you'll want to grab, plus this relates to your Energy Cell quest later on.
And now one of the simplest, most annoying puzzles in the game. Hillside Vista contains the Grapple Swing, but it's located on the other side of a gap. So how do you get across a gap to get an item that lets you swing across gaps? Like this:
Grapple Swing and missile upgrade - not a bad deal at all. Head back through the Grand Court via the passage by the golem's feet. Your new goal is all the way back at Gateway, through the one unvisited door that's still on your map. Swing across the gap to the downed ship, note that there's a missile upgrade above you for later retrieval (once power's running again) and activate the uplink as per your mission goals. When you're yanking the conduits back into place, be sure you do them one row at a time - you're making a complete circuit, after all. This downloads the map and opens up two new landing docks, both of which lead to your new goal - investigating two energy signatures that are powering the shield around the Phazon-oozing Leviathan.
Before heading to the Fiery Airdock, be sure to pick up the missiles like so: