After arriving on One Island and stepping out of the pier building, you'll meet Bill. Follow him into the Pokémon Network Center to meet his friend Celio.
Celio will task you with delivering a meteorite to the game corner on Two Island, and will give you this along with a Tri-Pass allowing travel to Two Island and Three Island. Return to the Ferry Captain in the pier building to go to Two Island.
After arriving on Two Island, walk east and enter the game corner building.
Inside, speak to Lostelle's Dad and he will give you a new quest of searching for Lostelle on Three Island.
Travel to Three Island by talking to the Ferry Captain at any island pier. Once there, follow the path north on Three Island until you reach a gang of bikers who are blocking it and talk to them. You will then fight them in a triple battle and face off against level 75 Pokémon.
After defeating and clearing out the biker gang continue to follow the path north, then west across Bond Bridge until reaching the entrance to the Berry Forest.
In the northwest corner of the forest is Lostelle. Talk to her and then battle the savage level 85 Hypno trapping her. After defeating it, Lostelle will return to the game corner on Two Island.
With Lostelle safe, return to the game corner on Two Island via the ferry and talk to Lostelle's Dad to deliver the meteorite.
Go back to One Island's Network Center and talk to Celio where you'll be given a new quest; find a gemstone on another part of One Island.
Exit the Network Center and follow One Island's path east. Talk to Jessie and James who are blocking the path to move them out of the way.
From here you will need to continue east by using Surf, then head north through Kindle Road. Keep making your way north until you reach Mt. Ember at the end of the road, then walk up the stairs to the mountain.
Walk up the first staircase to tutor Georg, then take the branching path east. Enter the cave into Ruby Path.
Follow the path inside until it branches, then walk down the south path; here will be two members of Team Rocket. Be prepared to battle Team Rocket Catty, a trainer who copies and uses three Pokémon of the prior player who battled her, at level 70 each.
Continue following the path west past Catty and head down into B5F of Ruby Path. Here in an item ball is the Ruby.
Exit the Ruby Path and bring the ruby back to Celio in the Pokémon Network Center. Upon delivering the ruby, Celio will give you the Rainbow Pass to allow travel to Four, Five, Six and Seven Island by ferry, as well as one last quest to complete the Sevii Islands main questline; locating a sapphire.
Talk to the Ferry Captain to travel to Six Island. Walk to the east side of the island to reach Water Path, then follow it south to Ruin Valley.
Inside Ruin Valley, go north and follow the winding path to reach the chamber in the center, Dotted Hole.
Inside Dotted Hole there are four floors, with four holes in each that must be fallen into in a specific order to reach the bottom.
The correct order, starting from B1F to B4F is: UP, LEFT, RIGHT, and DOWN.
After falling down the last hole you'll end up in the Sapphire Room, where the Sapphire will be in an item ball in the center of the room. Interact with it only to have it immediately stolen by scientist Gideon. Gideon takes the sapphire to Five Island, which is where you will need to go next by taking the ferry from the pier once more.
On Five Island, walk along the beach to the east to reach the Rocket Warehouse and meet Hacker Mitnick. He'll require you to defeat warehouse security on Four Island to gain further access, so go back to the Ferry Captain and sail to Four Island.
On Four Island, make your way to IceFall Cave at the northeast part of the island. Surf and Waterfall HM moves will be needed to navigate the cave.
Enter the cave and surf north to the waterfall, then climb it by using waterfall.
Take the ladder to the northwest down to the next floor, then enter IceFall Back Cave directly behind the ladder. Here you'll battle Team Rocket Ariana, who uses a full team of level 80 Pokémon.
After defeating Ariana, return to Hacker Mitnik behind the Rocket Warehouse on Five island. Cross Five Island Meadow and defeat the Team Rocket Grunts along the path. Upon finally reaching him, he'll need you to obtain 10 tools by defeating wild Pokémon in the Five Island Meadow grass.
Once all of them have been collected, he will tell you the password needed to open the warehouse door. This password is random and changes daily. Interact with the warehouse door and type in the password he tells you, then enter the warehouse.
NOTE: YOU CANNOT USE ANY ITEMS WHILE INSIDE THE WAREHOUSE. BE PREPARED BEFORE ENTERING.
Inside, use the upper row of arrow tiles near the entrance until you come to a stop, then follow the path in-between arrow tiles to reach Team Rocket in the northeast of the warehouse. Be sure to pick up the Nest Ball hidden behind a crate to unblock the path.
Before reaching Gideon, Jessie and James, Proton will stop to battle you with three Pokémon copied from the previous player, at level 70.
Proceed past Proton and confront Gideon and Team Rocket. Gideon will challenge you to battle, followed immediately by a double battle with Jessie and James with no opportunity to prepare in-between. These Pokémon will be level 85+.
Defeated, the group will hand over the sapphire which can now be returned to Celio in the Network Center on One Island. Deliver it and all Pokéboxes across the islands will now be accessible, and with that your quest will be complete!