In Batman: Arkham City, there are Riddler challenges, which comprise of things like predator (stealth) and combat challenges. Combat challenges have a scoring system which tallies up your score based on things like the types of moves that you used and how many different moves and gadgets used. I may complete all rounds without getting hit and without losing my combo streak, but I still won't score as high as the top 10 or so. How are such high scores achieved?
In the vanilla combat challenges (no DLC), there are a limited amount of bad guys per combat challenge. Each combat challenge is comprised of four rounds. Each consecutive round adds more bad guys and, in general, difficulty. At the end of each round, which occurs when all enemies have been dispatched, it tallies up the points that you've earned so far. Variations bonuses and such apply per round, so you may have gotten hit or lost your combo streak in one round, but you can still get bonuses for those in the other rounds. This combat mechanics guide will help.
The fewer enemies that there are, the harder it is to fit in all variations without incapacitating too many to prevent being able to perform all variations.
Step by step: I made acronyms to help me memorize the best order in which to perform the variations. My latest iteration (I modify this even as I post it), in its full form, is: CBSAGDLMFIUG. I would pronounce this as cob-sag-delem-fee-ug. Counter, Batarang/Bolas, Projectile, Lieutenant, Titan, Strike, Aerial assault, Gadgets, Disarm & destroy, Lesser-lethal special combos, Multi-ground takedown, beat-down Finisher, Instant takedown, Ultra-stun, Ground-pound. The routine is largely the same for Catwoman, who only ignores D.
Optimally, you're only finishing any enemy with special combo takedown, knife evade takedown or ground pound (because those finishing moves have the highest modifier (x100, x100, and x75, respectively)) and you're only finishing them when they have a sliver of health left. However, there aren't always knives to evade and electrified walls to move enemies into, and more importantly, unless you're super mindful, you can't keep track of how much damage each enemy has received or how much health that each has to maximize the points from each enemy. So, rotating beatdowns is the next best thing.
Putting it all together: Now, that acronym is hella long, and I find myself evading/redirecting until I run through the letters in my head. Here's a break-down by group: AGLF. Attack moves, Gadgets, Special combos, Finishers.
Is it ever better to just juice rather than fit in variations? After gathering data and running numbers, I've concluded little except that it's plausible that pure juicing, instead of variations, can be more profitable if your combo exceeds a certain point. I tried to craft a formula for calculating the difference in points earned from the two methods, but it's complicated. If you want to take a crack at the numbers, I post my jumbled analysis here: http://pastebin.com/5GryuHZz
Environmental projectiles: Of the projectiles that are thrown by thugs, gas canisters are set in certain combat challenge stages. Some only become allowed to be picked up by the enemy after a certain round. These can still be blown up at any time via batarang or bolas, even before their "activation" round. This is useful because blowing one up adds +1 to the combo count. Beware: Blowing it up when you're too close to it causes you to get hit by the explosion thus threatening to be a c-c-c-combo breaker.
I recently learned that there's an indefinite juice loop only with Catwoman and her bolas. Normally, moves don't count for points unless they damage, but the bolas won't deal damage at sub-x3 combo and award points on the hit that goes from x1 to x2.
Opinion: Once I learned that juicing beatdowns was necessary, I was like, "say it ain't so!" I had the same reaction to discovering the Catwoman indefinite. What I mean is, yes, getting a high score by juicing beatdowns is frustrating and the system seems too arbitrary. The case changes for the DLC combat challenges which are based on time or survival.
Update: From research that I conducted here, I've learned that it's also possible to indefinitely juice Titans.