The next upgrade is in Torvus, but it's near areas you've already been to so there's not really any new exploration involved.
Get to the underwater part of Torvus and go to the Main Hydrochamber; this is where you fought the Alpha Blogg. Go through the doorway opposite where you picked up the Gravity Boost, then Spider up the track to a portal.
Undertemple (Dark side)
Drop down and enter the main part of the room to start a boss battle.
Spider up to the top of the structure and grab the Power Bomb. These clear Yellow doors and destroy Benzium, and there are lots of both scattered around the game. The main problem with them is keeping topped up ammo; you only get two to start and the game is pretty stingy about dropping refills.
Blast open the Yellow door near where you picked up the Power Bomb to get out of the room.
You can either get back to the Light side via the portal here, but you may want to use another Power Bomb to clear the other Yellow and make a shortcut to the Undertemple Shaft.
Expansions (Torvus Bog)
There are plenty of new expansions to get now, and they're spread throughout the game. We'll cover the ones in Torvus first, then swing through the Temple Grounds, then cover Agon Wastes. There is an optional upgrade to collect there, covered in the next page, before returning to the Sanctuary Temple.
Go to the Gathering Hall; one way to get there is using the White door in the Hydrodynamo Station. You're going to need two Power Bombs for this so you might want to stock up ahead of time. Drop to the bottom of the pool and use a Power Bomb to break the glass floor. Now use another Power Bomb to break the plug underneath; this causes the water in the room to completely drain away. (Note that getting around here will be a bit different after this and you'll need to use the Grapple Beam to reach some parts of the room.) With the water gone, the floor is now a large half-pipe, so start boosting to reach one of the Spider Ball tracks on either side as for the Torvus Plaza Energy Tank. Follow a short Spider Ball course until you jump directly into a bomb slot. Activate the slot, then do the same thing on the other side of the half-pipe.
With both slots activated, a force field over a high ledge disappears and a ledge leading to it come out of the wall. Go to the door to Transit Tunnel West and use the Grapple Beam to reach the new ledge. From there it's a quick jump to get a Missile Expansion.
It's a short trip through Transit Tunnel West to reach the Training Chamber. Follow the Spider Ball track starting to the left of the Spinner; you have to do a couple jumps on the way. Drop down to a ledge in front of the statue when you reach the end, then activate the bomb slot there. The statue moves forward allowing you to reach a Missile Expansion.
Actually, you can get this expansion as soon as you have the Spider Ball, but there is a Yellow door you may want to clear as long as you're here. Chances are you'll have collected a Power Bomb from the Bloggs here. If so, then Spider up the track behind the Missile Expansion and blow open the Yellow door there. This eventually leads to Sanctuary Fortress, but we're not going there yet. Note that you can use the Gravity Boost to get out of the water and reach the door leading back to Hydrodynamo Station
Get to the upper section of Torvus and go to Torvus Grove. You'll need two Power Bombs for this so try to farm them on the way. Two of the tree trunks here, the mutated looking ones with thorns, have been weakened, so drop Power Bombs to destroy them and make the tree fall. If you single bomb jump near one of the trunks, a single power bomb will destroy both trunks at once. It breaks open a wall so you can reach a Missile Expansion.
Get to the Great Bridge; it probably doesn't matter much whether you go via Forgotten Bridge or Torvus Temple. If you're coming in from the Abandoned Worksite then you'll see a section of weakened rocks on the left as you enter. Otherwise, use the Orb Cannon to get to the bridge and notice a different section of weakened rocks at one end. Either way, use a Power Bomb to destroy the rocks and follow the tunnel; you'll get your first Power Bomb Expansion inside. The tunnel connects the two sections of weakened rocks, so you can either continue to the other end or go back if you want to save a Power Bomb.
Expansions (Temple Grounds)
We need to get to the Dynamo Chamber in the Temple Grounds, and if you're coming from Torvus then the shortest path is probably via the Great Temple. But we'll take the scenic route in order to pick up a scan on the way. So take the side path when you reach the Meeting Grounds.
When you enter the main area you'll notice that the Lumites that were here before have been replaced by War Wasps. In this case it's the Dark version though so you may want to collect a scan. Continue back to your ship where you can get a save in, and continue to Dynamo Chamber via the Temple Assembly Site.
You may remember that at the very start of the game, two gates closed behind you as you went through here. These made it impossible to get through again until you got the Space Jump Boots, and you still have to jump over them. We can finally clear them out of the way and get an expansion while we're at it. You'll need two Power Bombs so try to farm them on the way.
First, Power Bomb one gate to clear it, but don't bomb the other one unless you still have two bombs. Scan to find the weakened rocks in the tunnel, then bomb them to break open the wall. Collect the Power Bomb Expansion there, and now that you have at least one extra bomb you might as well clear the other gate (if you haven't already) so you have a shortcut through the tunnel.
The next upgrade is optional, so if you don't want to get it now then head back to Sanctuary Fortress, otherwise remain in the Temple Grounds.