Introduction
So I've been playing around a bit with Katarina and tried some builds listed here on MOBAfire (AD and AP) until i decided to try something different. Katarina has 2 abilities that scale both with AD and AP (
Bouncing Blade and 
Death Lotus), so why don't try out going hybrid? :) I know many people already tried out hybrid Katarina, but i wanted to leave here my 2 cents on the subject. :)
Keep in mind that this guide is supposed to be a GUIDE, not a formula, so things may not turn out as you expect them to.
Thank you for checking out my guide and let's proceed :)
Masteries
As for masteries go, i take the 9/21/0 mainly because of 
Shunpo, one of your main abilities. When you use it to go to the middle of a fight, you're prone to take damage and being focused on, so you need to able to soak some damage, and the points in defense really help a lot, specially early game. The points in offense are self-explanatory, 
Exhaust for chasing, crippling and also the magic reduction debuff is nice, and 
Archaic Knowledge for more magic penetration.
Summoner Spells
These summoner spells, in my opinion, are a good combo for Katarina because with Exhaust you can: reduce magic resistance, slow, cripple the opponent, etc.. and with 
Flash you can tower dive (when possible) and flash away, or flash in range of your Shunpo for that last hit or to safety, the basic "get-in-places-fast" skill.
Bouncing Blade
Okey, when using Bouncing Blade you need to know where to aim at! I have some images to try explain a little better what i mean with aiming.
So, when in a standard 1vs1 (and even 2vs2) situation, where you have minions fighting in the middle and the enemy champions somewhere between their melee creeps and behind caster ones, you can try to aim like this, to harass them:
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Other great time to harass, is when the new wave of creeps is coming, and they're lined up. When this happens, you want to get the enemy champion out of fog of war and near the minions, so you can do like this:
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Use to harass a lot, since it's on a very low CD and with this build you take out nice chunks of health from you opponents.
Team Work
As for team work goes, you just have to love stunners :) having an ally make your enemy stand still as you pop Death Lotus is just sweet! ^^ so nice champs to have on your team are 
Sion, 
Sona, 
Taric, 
Evelynn, etc etc.. Even 
Galio with his ulti! :p
One other thing, because you're always jumping from enemy to enemy and you're ultimate shoots very fast, you may end up being called kill stealer and such, but hey, it happens, so don't worry! Specially when you go triple kill, and the enemy team surrenders. ;)
Playstyle
I like being very aggressive with Katarina, even though i'm mostly in the back, behind the tanks and tanky DPS', unless when solo.
One thing is certain with Katarina, you can't simply pop 
Killer Instincts, Shunpo to the middle of the fight and pop Death Lotus and expect a penta kill!! You have to play smart!
Everyone is doing a stand of? Harass with Bouncing Blade until the fight begins. Wait for the other team to blow out most of their disable spells, such as stuns, silences, knock-ups, etc, or one of 2 things happen:
A) They don't know how to play and leave you spinning and melting their HP
B) They'll focus you, and you die
So when going into a fight bear in mind 2 thing, first, that you're not going kamikaze! Make sure you have an escape strategy and second wait for the disables to be used. That way you'll have more chances of being successful with you're ultimate! :)
Summary
Hope this will help you with a "new" approach to playing Katarina. Feel free to vote and comment, as opinions, suggestions, errors that you point out, ways to improve the guide, etc, are always welcome! :)
Thank you for reading my Katarina, the Hybrid Way guide,
Hikas @ EU
Build Guide
Discussion (10)
Greater Mark of Insight
Greater Seal of Evasion
Greater Glyph of Focus
Greater Quintessence of Insight
Greater Seal of Resilience
Greater Seal of Fortitude
Greater Glyph of Warding
Doran's Shield, and selling it when there is no more room, for the 6th item. But if you're comfortable with playing Katarina, and believe you can do well with her, feel free to try out this other set of items (the ones i use mostly now):
Long Sword -> 4- 
Sword of the Occult
Boots of Speed -> 2.1- 
Sorcerer's Shoes (if already have the money for it, i buy it straight away
Amplifying Tome -> 5- 
Mejai's Soulstealer
Giant's Belt -> 7- 
Rylai's Crystal Scepter
Warmog's Armor
Hextech Gunblade
Banshee's Veil ) if you're being really focused on, or 
Void Staff if they are stacking MR. Remember, always build according to the other team.
Infinity Edge and the 
Rabadon's Deathcap which provide a solid AD and AP to work with.
