You have 3 choices of challenges:
 - Multi Battle
 - Single/Double Battle
 - Wi-Fi Battle

Multi Battle
     Here you will be taken through the elevator to an underground room. There, you choose your partner. Your choices of partners are of the many people you have teamed up with in multiple parts of the game(They will not show up here unless you have already teamed up with them). You are allowed only two pokemon as is your partner.
     Your partner choices, their pokemon, and their team up locations are as follows:

Cheryl - Eterna Forest
 Pokemon: Snorlax, Espeon, Umbreon, Porygon2, Blissey, Milotic, Latias, Latios, Gastrodon, Porygon-Z, and Cresselia

Mira - Wayward Cave(Main)
 Pokemon: Alakazam, Gengar, Zapdos, Espeon, Gardevoir, Latios, Roserade, Magnezone, Magmortar, Togekiss, Glaceon, and Porygon-Z

Riley - Iron Island
 Pokemon: Poliwrath, Machamp, Rhydon, Gyarados, Ursaring, Tyranitar, Blaziken, Breloom, Slaking, Hariyama, Medicham, Absol, Salamence, Metagross, Rampardos, Lucario, Toxicroak, Rhyperior, Mamoswine, and Regigigas

Marley - Victory Road(Post Elite Four)
 Pokemon: Dugtrio, Electrode, Starmie, Aerodactyl, Crobat, Sceptile, Swellow, Ninjask, and Weavile

Buck - Stark Mountain
 Pokemon: Umbreon, Forretress, Steelix, Shuckle, Skarmory, Regirock, Regice, Registeel, Bastiodon, Rhyperior, Probopass Dusknoir, and Cresselia

Choose your partner wisely as they will only have two of their pokemon. You should talk to them all because they will tell your their pokemon and one move of each of them. After your choice has been made go to the elevator and the woman will bring your and your partner up to take your challenges. You will face 7 trainers. If you win you will get battle points to spend at the shop in Battle Park.

Single/Double Battle
Here you have a choice to take a single or double battle challenge.
 - Single Battle
     You are allowed to bring 3 pokemon in with you. No matter what level your pokemon is they will be reduced to lvl 50(I'm not sure if any pokemon are raised to level 50 unfortunately.) You go through 7 battles each challenge.

     If you manage to do a 20 battle streak without losing you will face the Tower Tycoon, Palmer, on your 21st battle. A warning that the 3rd Single Battle challenge will get very difficult as your near Palmer. Due to that I have never been able to face Palmer myself. His team is as follows:

Tower Tycoon Palmer 21st Battle
 - Dragonite
 - Milotic
 - Rhyperior
Recommended Types: Ice, Grass, Dragon

     Also when your reach a 48 streak without losing on the 49th you will face Palmer again but with a full team of legendaries. This team is as follows:

Tower Tycoon Palmer 49th Battle
 - Heatran
 - Regigigas
 - Cresselia
Recommended Types: Water, Fighting, Dark, Ghost, Ground

Defeating Palmer Earns you 20 battle points. If you defeat Palmer give yourself a pat on the back and keep on battling.

Double Battle
This runs the same as Single battle but you get to bring in four pokemon and you use two pokemon at a time as does your opponent. I believe Palmer also does not show up here. You get battle points for completing each set of 7 trainers.

 - Wi-Fi Battle
     This runs just like Single Battle except you download a room off of Wi-Fi. It downloads a room of people who have uploaded their teams to Wi-Fi. This works like all the other challenges. You fight in a set of 7 and fi you clear it you get battle points.

     Now that I've explained the challenges I only have a little more left to explain.
     Primary Business for all challenges like this since the battle frontier, banned pokemon. Here is the list:
 #150 - Mewtwo
 #151 - Mew
 #249 - Lugia
 #250 - Ho-oh
 #251 - Celebi
 #382 - Kyogre
 #383 - Groudon
 #384 - Rayquaza
 #385 - Jirachi
 #386 - Deoxys
 #483 - Dialga
 #484 - Palkia
 #487 - Giratina
 #489 - Phione
 #490 - Manaphy
 #491 - Darkrai
 #492 - Shaymin
 #493 - Arceus
Those are there for you so you can plan the perfect team without breaking the ban.

Our final order of business: Items For Battle Points and their costs. As you can get battle points from the Battle Tower challenges. They are exchangeable for items unobtainable anywhere else in the game or obtained very scarcely throughout the game such as the Legendary Rare Candy. Here is the list:

Item            Cost
Protein.........1BP
Calcium.........1BP
Iron............1BP
Zinc............1BP
Carbos..........1BP
HP Up...........1BP
Power Bracer....16BP
Power Belt......16BP
Power Lens......16BP
Power Band......16BP
Power Anklet....16BP
Power Weight....16BP
Toxic Orb.......16BP
Flame Orb.......16BP
White Herb......32BP
Power Herb......32BP
BrightPowder....48BP
Choice Band.....48BP
Focus Band......48BP
Scope Lens......48BP
Muscle Band.....48BP
Focus Sash......48BP
Choice Scarf....48BP
Razor Claw......48BP
Razor Fang......48BP
Rare Candy......48BP
TM06Toxic
TM73ThunderWave
TM61Will-O-Wisp
TM45Attract
TM40Aerial Ace
TM31Brick Break
TM08Bulk Up
TM04Calm Mind
TM81X-Scissor
TM30Shadow Ball
TM53Energy Ball
TM36Sludge Bomb
TM59Dragon Pulse
TM71Stone Edge
TM26Earthquake

Credits
Serebii for the stats and pokemon of Palmer and the Multi Battle Partners
My DS
My Pokemon Pearl
Nintendo
My patience

If there are any problems with anything on this FAQ email me at Bentheechidna@hotmail.com
or contact me at Deviantart.com as Bentheechidna