Kha'Zix early dueling is not horrible, especially if the target he is dueling is isolated due to his Passive. But if you catch him during his first clear, he will be low health due to his unhealthy clears.
The same concept of isolation pertains to when you get ganked by Kha'Zix. If you try running away and isolate yourself from minions, he will deal much more damage to you. Try and huddle around minions until he uses his Wings (E) so you can escape.
Make sure to ward objectives because if Kha'Zix takes his Reaper Claws (Q) evolution first, he can easily solo objectives in no time.
In team fights, make sure to keep your carries close to other players on your team. In doing so, you mitigate a lot of Kha'Zix's damage by not being isolated.
Purchase a Red Trinke as when Kha'Zix goes into stealth you will be able to see where Kha'Zix is- eliminating his surprise factor.
Crowd control is a necessity when playing against Kha’Zix as it reduces his assassination and jump potential. Try to lock Kha’Zix down as soon as he jumps in to prevent him from getting in and out.
Kha'Zix power spikes at level 6,11, and 16 as those are the levels he can evolve an ability.
Kha'Zix has a power spike when getting his Warrior Enchantment because this increases his damage output and duelling potential.
Another large power spike for Kha'Zix is when he gets his Duskblade for a number of reasons. Firstly, it gives him extra damage and duelling potential. It also allows him to one-shot squishy champions he can catch roaming the rift.