It can save a little time if you have a Pokemon with Strength in your party. As you travel north to the Dragonspiral Tower, you will be stopped by Bianca. Cedric will say Team Plasma broke through the tower wall. He gives you the Old Gateau, which heals any status effect. Walk north through the passageway. You can Surf in the water east of the tower entrance. There is an Ace Trainer waiting for you.
That's all there is to do outside so enter the tower.
Follow the path northeast to the stairs. The ground will shake as you approach. Travel up the stairs to the second floor.
Take a step forward and Cheren will let you know you can walk on fallen columns. Walk on the west side of the fallen column in front of you and there will be a big boulder to push using Strength to the north. East of the big boulder, underneath a suspended column, is a Hyper Potion. Either use the fallen column on the east side of the room or use Strength on the boulder to get to the western doorway. There is a Stardust to pick up south of the stairs. Walk through the doorway.
Walk up the stairs. This area is filled with one-way ledges. Walk down over the first ledge. Now there are three ledges to the left. Walk over the bottom one and then the next two to the left. Walk up on the following one and continue going up, up, right, up, and right to find a Shiny Stone. Use the same path this time, but go up the next set of stairs and through the doorway.
Cheren and Brycen are on this floor holding off some Plasma Grunts for you. Battle the grunt south of Cheren.
There is a Dragon Fang down the set of stairs to the east. It increases the power of Dragon-type attacks by 20%. Go up the northern stairs to the 5th floor.
This is a psuedo-3D puzzle invloving ledges. Walk right until you find the stone walkway to cross. Walk left to the next walkway and cross it. There is a Star Piece before the ledge. Hop over the ledge and continue right until you hit a wall. Walk down across the two stone walkways and left to find a Stardust. Walk up through the two walkways again, walk left, and walk up the walkway to the center of the room. Go right and hop over the ledge. Walk down over the walkway and move left to use the next walkway down. Walk right until you find a Revive. Walk back to the left and use the next walkway down. Use the stairs to the left to enter the 6th floor.
The ground will shake again after you take a few steps north. Follow the path north to find a Max Elixir. Now would be a good time to save. Walk west to find Giallo, another Team Plasma Sage. He will tell his four grunts to battle you one by one.
Walk south and up the stairs. Walk north to see N standing in front of Zekrom in Black, or Reshiram in White. The legendary Dragon-type Pokemon flys away and N says you will eventually meet the other one. Zekrom/Reshiram will swoop down and fly away with N. Cheren and Brycen appear and take you back to the beginning of the Dragonspiral Tower with Cedric and Bianca. Alder eventually shows up and tells you to head to the Relic Castle off of Route 4.