To rescue the Bicycle Shop Manager in Pokémon Brilliant Diamond & Shining Pearl and progress, you’ll have to defeat Team Galactic. Here’s more detail on how to do that.
The building itself can be found at the top right of Eterna City, and is fairly easily to navigate. Unlike more Galactic buildings you’ll come across later, there are no warps - yet. Just take the stairs to each room and defeat the grunts you come across along the way.
You can keep returning the Pokémon Center between battles if you need to, and will be able to heal your Pokémon. If you’re impatient, you can take items into the building with you and use them between battles. Due to the fact this building is so easy to navigate, however, you don’t really need to worry about any issues with exiting and re-entering.
The battles themselves shouldn’t prove too difficult. If you’ve leveled up your Pokémon enough, they’re pretty easy to get through.
Chimchar (and their evolutions) will be very handy for taking out the Bug-type Pokémon (and you should do so quickly, to avoid their poison moves). If you don’t have Chimchar, the battles may be a little tougher but still very doable at this stage of the game without having to go back and grind.
If you caught a Shinx early on, they’re great for taking out Zubats. You should also do this quickly, as they can cause Confusion in your Pokémon and make the battles a little more of a slog.
The Pokémon to watch is the Kadabra, sent out by the scientist. You’ll be able to tell it’s coming because the scientist looks different from the grunts.
This time, if you started with Chimchar, it’s time to hold off. Kadabra is strong against Fighting-types, and you likely have a Monferno now, who is weak to those moves. Kadabra’s Psychic-type moves can deal a considerable amount of damage.
Galactic Grunt & Galactic Grunt (Double Battle)
The Boss: Commander Jupiter
The last person you’ll fight in the building, on the top floor, is Commander Jupiter. As you might expect from a Galactic boss, she proves a little more difficult than the other trainers in the building.
Her Zubat is easy to take out with an Electric-type move, but her Skuntank can be hard to knock down. It’s weak against Ground-type moves so if you have any Pokémon who know some, send them out. Zubat will be first, though.
After you’ve defeated Commander Jupiter, the Bicycle Shop Manager will return to his shop in Eterna City. Go find him to receive a free bike as thanks, and you now cycle to your next location.