What are all of Batman's combat moves in Batman: Arkham Asylum?
The moves you have to perform in a single combo are (PS3 / 360 / PC):
Strike (Square / X / Mouse Left)
Counter (Triangle / Y / Mouse Right)
Cape Stun (Circle / B / Mouse Middle)
Evade (X x2 / A x2 / Space x2)
Throw (Square + X / A + X / Shift + Mouse Left)
Takedown (Triangle + Circle / B + Y / Shift + Mouse Right)
Ground Takedown (R2 + Triangle / RT + Y / Ctrl Left + Mouse Right)
Batarang (L1 / LT / Q)
Batclaw (R2 x2 / RT x2 / C)
As far as which order and where to do it, I would check sites like True Achievements (Xbox 360), or PS3 Trophies Forums for some tips. Check YouTube as well, there's loads of videos for it and a bunch of different possible solutions.