how do i play tank katarina top

you dont

I don't know what you could take to make her a little more tanky and still be effective, but Assassins and Marksmen generally can't build towards tank without lowering their effectiveness severely. Some can and do well depending on what their abilities scale with, but the point is to generally do as much damage as possible.. building more than a little sustain hampers that ability usually. Her kit specifically is designed to hop in, do as much damage as possible, and hop out, never needing more than just the typical health/armor/MR from the more damagey (that's a word) items, like Zhonya's for example. Because of her ability to essentially flash away without a delay, building her tank is almost wasted.

Just my two cents.

I haven't taken on a full "Tank Kat" build myself, but Kat's base ratio's aren't all that grand. W/E are both .25, Q is .6. Could be worth trying out an MPen build on her. You just start with the MPen trinity (sorc shoes, haunting guise, abyssal) and then build whatever tankier items are appropriate against the enemy team. You rely more on base damages than raw AP. It also works for Lissandra (highest ratio being .7) and AP tanks like Malphite.

I'm not sure of top katarina, but jungle katarina can first clear as fast as shyvanna about 2:50-2:52 with the right runes and buy her jungle item, its different because you use your W to reset your auto's, you could go abit tanky actually though, as a sight stone would help you with escapes well also shanpo wanted to say shampoo :P to your monsters or enimie monsters and also have bizzare ganking strategies most won't see coming.