Archen
Movepool: It starts with Ancient Power (you can TM Rock Tomb), learning Acrobatics (its best move) 3 levels later at 28 to replace Pluck. Archen gets Crunch at 35, U-Turn at 45 and Rock Slide via TM. Dig, Focus Blast and Dragon Claw are options, but the line will be mostly use Acrobatics.
Probably a tweak needed to the grammar above, mainly "using acrobatics"
Axew
Typing: Dragon-type is practically unresisted due to Steel, Ice, and Dragon-types being rare (outside of Brycen and Drayden/Iris for the latter two). Dragon typing is also great defensively, as it resists Grass, Fire, Water, and Electric.
Movepool: Axew will have Dragon Claw upon being caught. It learns Dragon Dance at level 32 and Swords Dance at level 48 as Fraxure. It can also learn Brick Break, Shadow Claw, and X-Scissor through TMs as Haxorus as rotating coverage depending on which Trainer you fight.
Typing section is confusing, Dragon is only resisted by Steel. Small tweaks might be needed for the movepool section; "TMs as Haxorus for rotating coverage".
Throh
Availability: Early-game (10% chance to appear in grass (White) or 5% chance to appear in rustling grass (Black) in Pinwheel Forest (Outer)).
Typing: Fighting gives it an advantage against Lenora, Brycen, Grimsley and a resistance to Burgh's Bug-type moves, but it is threatened by Skyla and Caitlin type-wise. Its Fighting STAB is also ineffective against Shauntal's Ghost-types.
Stats: Throh possesses high Attack and HP along with good Defense and Special Defense, but it is rather slow.
Movepool: It will have Seismic Toss upon being caught and, based on level, Vital Throw (otherwise learnt at level 17). More damaging moves in the form of Revenge, Storm Throw, and Body Slam are learnt at levels 21, 25, and 29, respectively. Bulk Up comes at level 33 and Superpower at level 49. TM-wise, it can be taught Brick Break (outclassed by Storm Throw) and Rock Slide. Payback via TM helps Throh do well against Shauntal.
Major Battles: Throh is really useful against Lenora. It also sweeps all Gym Leaders, even Skyla and onwards, thanks to Bulk Up. Against the Elite Four, it can sweep Grimsley and Marshal reliably, while Shauntal has her team swept by Throh, minus Cofagrigus, if you heal it up a few times. It is also useful against N and Ghetsis, as it can take down a few of their Poémon easily.
Additional Comments: In White, you can find a level 17 Throh fairly easily by going into dark grass with a level 17 Poémon in the lead and using a Repel. Throh generally can set up only 2-3 Bulk Ups at most, as its low Speed means that it will often take a hit before doing anything.
You mention Bulk Up a lot in this analysis, and I am wondering if its worthy as an A rank mon if it absolutely needs to set up vs most principle trainers in order to stand a chance. Most of the other Pokemon here can just push on without any issues, whereas it reads like Throh needs 2 turns to be scary vs opponents. Setting up while healing is inherently not very efficient, so I think it should drop to B based on the above description. If it doesn't need so much reliance on Bulki Up, its fine where it is