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Don't worry about only trying to hit the backline carries, your W will chunk the frontline too. Only get close to autoattack enemies when it is completely safe, or when you have your team near you. Try to rely on your W for constant damage. Your W can easily 2-shot carries if they have no MR, with a W, R+W combo. Learn how to walljump with Kai'Sa ult. Make sure to proc your caustic wounds with W and autosttacks whenever anyone has multiple stacks of plasma on them. Sometimes it's better to E or protobelt to get close and burst an enemy, and then RW to finish them off. Try not to miss your Void Seeker, since it heavily affects your total damage output if you don't get a cooldown refund. Look to poke the enemies from far away, and use any friendly CC to ult in and R+W squishy enemies. Q evolve is enough to easily solokill enemies by yourself while W evolve makes you a strong teamfighter due to your low W cooldown.
You are fully online at Manamune + Pickaxe + Hextech Rocketbelt + Amplifying Tome where you will have Q and W evolve, and a ton of ability haste from boots and runes.
By the time you ult in, your W should almost be off cooldown. Catch out stragglers with your W and R.Since you will often have lane priority, try to roam and help your jungler in skirmishes, establish deep vision, or gank a side lane.1 evolved Icathian Rain is enough to delete the first 3 melee minions, and you can autoattack and/or Q the leftover minions. This will give you Q evolve, letting you easily clear a wave. Focus on farming for your Manamune + Pickaxe.With the earlier level 2, you usually can gain control of the lane minions and go for a cheater recall.
The enemy will reach the same level 1 minion slower. You will hit level 2 off the first wave so use that to force a good trade against your level 1 opponent.
Use the raptor trick to gain an early XP advantage if you started Doran's Blade.