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This guide is for new game plus although it might be useful for standard playthrough as well.

The strategy I used throughout entire fight, to keep it simple and consistent, is this: evade (jump over) and punch ONCE. When your combo gets high enough to do a takedown do it straight away. For the most part Deathstroke won't cause any problems but sometimes he will attack and this is where the biggest challenge is - don't block straight away! Keep it together and wait for slow motion, it's really obvious when to block if you pay attention. Block just once per słów motion attack. In the first section of the fight he will attack just once, in the middle twice and at the end three times. Just keep it cool, pay attention to slow motion and you'll be fine.

These three sections I've just mentioned are separated with a special sequence which begins with a flash and follows with him jumping down on you. Here you don't have to worry about timing, just spam block until you head butt your opponent and follow with beatdown. Remember to use your beatdown combo to do a takedown afterwards.