If you're having trouble clearing Arkham City's Top of the World Extreme challenge map, here's a set of instructions on a fast, easy way to not only grab two of the three medals right off the bat, but also to get rid of the Detective Mode Jammer.
From your starting position, grapple to the gargoyle directly above you.
You should see an armed thug on the balcony below you.
Wait until he turns around, then drop off the gargoyle and grapple to the edge of the balcony.
Wait until the armoured jammer thug inside moves behind the pillar (so he can't see you) and do a ledge takedown on the guy on the balcony.
Immediately grapple to either the left or right gargoyle, and then swap to the other side of the balcony. This is because two thugs might see you grappling, and target the first gargoyle you climb onto -- but if you swap gargoyles, they won't find you.
Now, unfortunately, there seems to be no reliable way of telling which of the two thugs will be on which side of the balcony. If you're on the wrong side, you'll have to restart the challenge. That's not too big a deal, though, since you should only be thirty seconds into the challenge at this point.
Anyway, you want the jammer thug to be the one closer to you...
...so that you can hit him with an REC charge and knock him into his buddy for the first medal.
Toss a smoke pellet at the two thugs.
Glide down and perform a beatdown on the armoured thug.
You now have two of the three required medals and can use Detective Mode freely. This should make the rest of the challenge much easier.
if you can. Freeze the henchman, punch him and do a quick ground takedown. If it proves to be difficult to do the beat down. The thing is to take down the jammer.
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