I just spectated your Katarina ranked game, the one where you were mid vs Wukong. I came in a bit late, so I didn't see how it happened, but you were 0/4 as the laning phase ended and you had pretty low farm when I came in and throughout the game.
If you want to make it out of Bronze, you will want to place a lot more emphasis on paying attention to enemy abilities. Even though their team had
ult,
ult,
Q & W, and
W to interrupt your ult, you were pretty eager to immediately hit QEWR as soon as the fight started. You have to be more aware of ability cooldowns. It makes perfect sense that anyone on the enemy team who has one of those abilities will use it on you immediately as soon as they see you Shunpo into 5 champions. If you want the full ult duration you will need to wait until another threat on your team is being dealt with. Alternatively, you could have picked up a BV to soak up one of those 5 abilities.
You also (along with your team) made a pretty big mistake repeatedly: sieging mid lane after the inhib is down. You guys had so many needless deaths inside their base because you kept walking up to their nexus turrets with no goal in mind. There was a point where 4 of you were in their base, 1 died, 3 (including you) were escaping at very low health. Inexplicably, when your two allies got caught and killed, you turned around to Shunpo back in on full health targets just so you could flash over the opposite wall. You would have lived if you had just kept running, but Corki flashed after you and got the quadra (and then got the penta on your last guy). You want to have situational awareness at all times. Since Kat really just has a GO button and nothing else, 99% of your attention can be dedicated to watching the map and being aware of where each champion is, what their health is, how much of a threat they are, what abilities they have available, etc. In that situation, there was nothing to be gained by going back in.
These skills are far more important than the particular champion you're playing. It doesn't need to be an assassin. Any champion will get you to Silver if you learn all the important aspects of the game.