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Hi Everyone! ^^ This is Kitty, and this is my first time writing a guide. I am currently a plat 3 player who main mid ap champions. I personally prefer mid assassins who are very mobile and can gank other lanes easily.

Katarina is one of my favourite champions. She is a very mobile assassin, and her passive refreshes her skills whenever she kills an enemy champion. What I love about tanky Katarina, is that she is extremely hard to kill and still does damage. You don't have to worry about when to go in a fight, because as tanky Katarina, you can initiate a fight. Her global taunt is also very strong, the enemy team will always try to focus and kill you first in team fights.

Pros:
Extremely hard to kill
Tanky and still does damage
Very mobile, and cooldowns are low
Global taunt makes everyone focuses you first even when you're really tanky
Don't have to worry about when to go in during team fights, you can initiate.


Cons:
Not much burst damage
Weak early game against other high-damage assassins (Etc Jax, Zed)
Ult is easily interrupted, which reduces her damage output.

Let's talk about runes first.
My runes for tank Katarina:

I use magic penetration runes for red, because Katarina's abilities do magic damage. Magic pen helps to deal more damage to enemy champions. This extra magic penetration also helps Katarina to easily kill the enemy ad carry with Bouncing Blade and Death Lotus.
I choose armor runes for yellow, since Katarina needs the armor to solo top or against any ad champions.

The best part about Katarina is her passive. When she gets an assist or a kill, all of her ability's cooldown is reduced by 15 seconds. This passive gives Katarina the ability to snowball and to carry the team. If she gets kills she can almost spam her skills in team fights.
Basically Bouncing Blade is Katarina's most important ability. This ability does the most damage to enemy champions. Whenever an enemy unit is hit by this ability, the unit is marked, and Katarina can trigger the mark to deal damage by basic attack, or using another ability.
sinister steel This ability deals damage to surrounding units, and gives Katarina bonus movement speed whenever it hits an enemy champion. What I love about this ability is that it has a relatively low cooldown, gives bonus movement speed, and it can also be a skill that is used to clear minion waves or trigger Bouncing Blade.
This is what makes Katarina fun to play. It can be cast on allied units or on enemy units. Basically you can use this ability on anything. In lane, you can cast this on minions to escape a situation, or you can cast this on enemy champion to deal damage.
Like every other ultimate, Death Lotus is also a great ultimate which has a relatively short cooldown. You want to use this ability when you see the enemy champions have used their crowd control abilities to maximize your damage. This ultimate can be stopped by any hard crowd control abilities. (Etc：stuns, silences, knock ups, fears, Static Field, Rupture)


Katarina is very dependent on her Bouncing Blade and Death Lotus to deal damage. Always get Death Lotus whenever you can(At level 6,11,16), and max Bouncing Blade first for the damage. Max sinister steel second for its speed buff whenever it hits an enemy champion. (Note: If you are having trouble farming or the enemy jungler keeps ganking you because your lane is always pushed, try to max sinister steel first so your lane won't be pushed whenever you try to farm with Bouncing Blade) I recommend maxing Q Bouncing Blade for extra damage over W Sinister steel.
Katarina's E Shunpo is basically used for escaping or gap closing, it does not provide her with lots of damage. I recommend maxing Shunpo last, but always get it at level 2, or level 3 for its effective escaping/gap closing ability.