this achievement can be tricky, as we've all seen throughout the past batman games. however doing this on the gotham knights challenge (the one with knightwing) can make things a bit easier, because there are no brutes to break your combo and no electric enemies, however shield carriers do spawn later on so be careful.
the moves are:
3.throw counter-left stick towards enemy+Y
5.super stun-B,B,B/hold B(i'm not sure whether these are the same move but odds are you probably won't use it anyway due to the time it takes to charge)
8.batclaw into aerial juggle-LT+Y,B,X
13.ground pickup into beatdown-RT+B,X repeatedly (again i am not sure whether this is any different to the regular beatdown)
takedowns (some of these will require upgrades):
17.batclaw takedown-LT+Y hold
18.electric takedown-LT+B hold (doesn't actually take enemies out)
19.explosive gel-LT+X hold
20.batarang takedown-LT hold
21.freeze bomb takedown-RT,RT hold
22.ground area takedown-A+B (with enemies on the ground)
24.environment takedown-A+X (when enemies glow blue)
25.dual takedown- LB (when meter next to bat symbol is full)
25.you can also do a batmobile assisted takedown but not in this map, and it is exactly the same to pull off as a environment takedown.
as you can see there are more than enough to get fifteen, and i have a feeling that i am missing some. a few tips:
.use evade (A,A) to give you time to think about your next move, it will not reset your combo
.try not to use super stun, holding B will take too long and when i went to use the 3 Bs i would always target a different enemy on the third stun, this would reset my combo.
.be careful of the shield enemies when they spawn on this challenge map hitting them will reset your combo, this would be a good time to use the ground pound (see above) if you haven't already.
.try to avoid using more than 1 quickfire gadget in a row, as sometimes you will just end up aiming your current gadget which will reset your combo.
please let me know if i am missing something or if i have gotten something wrong.
the achievement will probably take a few tries and i would recommend restarting if you get hit or drop your combo, because there are a limited amount of enemies in this area