I've had most of the following records for a while, so I've forgotten a lot of details regarding how I lost in most of the facilities. This team has a rather severe ice weakness though, so I'm going to bet that that had a big thing to do with most of those losses that I don't remember.
My goal when starting this streak was just to get the colored prints from each facility, the 100-streak star for my trainer card, and the 50-streak ribbons for my starter. I basically just copied
Samhain Grim's team and strategy, as I had already bred a similar Gengar and Garchomp and could easily replicate his performance. Team info first, records below:
Togekiss
Item: Leftovers
Ability: Serene Grace
Nature: Calm
IVs: 29/31/15/31/19/7
EVs: 255 hp, 255 spdef
~ Air Slash
~ Aura Sphere
~ Thunder Wave
~ Roost
Team lead for the Tower/Arcade/Castle (single). Paralyze, flinch, stall, win. If the opponent sends out an electric type, switch to Garchomp.
Gengar
Item: Focus Sash
Ability: Levitate
Nature: Timid
IVs: 28/27/31/30/31/31
EVs: 6 hp, 252 spatk, 252 speed
~ Shadow Ball
~ Thunderbolt
~ Focus Blast
~ Destiny Bond
Team lead 1 for doubles. Kill whatever possible, then Destiny Bond.
Garchomp
Item: Yache Berry
Ability: Sand Veil
Nature: Jolly
IVs: 4/31/24/31/29/31
EVs: 6 hp, 252 atk, 252 speed
~ Aerial Ace
~ Earthquake
~ Outrage
~ Swords Dance
Team lead 2 for doubles. A fast Earthquake + Levitate combo wipes out so many CPU doubles teams that things really go by rather quickly. Outrage was usually only used as a last-shot desperation move when 'Chomp was at low HP. Aerial Ace and Swords Dance were hardly used at all, and if I were to do this all over again I'd probably replace them with something else.
Torterra
Item: Life Orb
Ability: Overgrow
Nature: Adamant
IVs: 12/30/4/23/19/21
EVs: 252 atk, 6 spdef, 252 speed
~ Earthquake
~ Wood Hammer
~ Stone Edge
~ Crunch
My in-game starter converted to an adequate battler. He was only used for doubles games and in specific milestone streaks in the Tower in place of Garchomp. My goal was to collect all 39 possible Sinnoh ribbons for him including those earned from the Battle Tower, so I'd bring him in when facing the Tycoon or when reaching the relevant 50-streak milestones. While his speed is a significant drawback, he didn't do so bad.
Records (all on Platinum):
Battle Tower Single: 116 (Togekiss, Gengar, Garchomp/Torterra)
Battle Tower Double: 61 (Gengar, Garchomp, Togekiss, Torterra)
Battle Tower Multi w/CPU: 67 (Garchomp, Torterra)
Battle Tower Multi w/Friend: 50 (Gengar, Garchomp, Togekiss, Torterra)
Battle Tower Wifi: 15 win streak + Rank 5 (Togekiss, Gengar, Garchomp/Torterra)
Battle Factory Single/Open: 51
Battle Arcade Single: 50 (Togekiss, Gengar, Garchomp)
Battle Castle Single: 50 (Togekiss, Gengar, Garchomp)
Notes:
Tower Doubles - In my loss, the opponent used a Latias and I kind of panicked, focusing too much on killing it quickly as possible and not thinking things through very clearly. The match was over once the opponent's Starmie froze my Togekiss before it was able to do anything. Video of this battle: 76-46244-32839
Tower Multi w/CPU - I basically just go for the Earthquake + Levitate combo with either Mira (Special Attack) or Marley (Speed). EDIT: Just finished this streak at 67 wins. Video ID is 14-97385-47262. Highlights of this loss include: me forgetting to put Life Orb on Torterra, me forgetting that one of my two teammates did not have an EQ immunity, my ice weakness catching up to me again, and Mira basically playing like an idiot.
Tower Multi w/Friend - I did this streak by myself using a friend's DS and his copy of Diamond with my Platinum copy serving as the host. Same exact strategy as my Tower Doubles run, but I purposely ended the streak after the 50th match because I was afraid of losing the streak to a communication error, which had already happened twice in prior attempts.
Tower Wifi - This team really doesn't fare too well against the wifi teams, so I'd rarely win more than 1 streak in a row. I quit after reaching Rank 5.
Factory - Worthy of its reputation as the most frustrating facility in the frontier. I finished this record a long time ago so I don't remember how I lost, but I do remember that I got lucky by receiving a Latios at the very beginning of my 7th streak and basically just demolishing almost everyone including Thornton with it. After obtaining the colored print, I stopped painstakingly using the reference material in the OP to research my opponents' teams and just played blind to a quick loss.
Arcade/Castle - Basically used the same strategy for the Tower, stopped caring once I got to 50 and started playing sloppy. I think I was way too conservative with CP in the Castle.
Again, sorry that these descriptions are light on details. I didn't bother posting them when most of these were recent because they were just retreads of Samhaim's team and strategy. I only just noticed that there aren't many records for some of the Tower game styles and decided I may as well just post mine to put something up there.