Your main goal needs to not be climbing, and that is realistically the best advice anyone from any rank or division can tell you.
Play to improve and you will climb naturally
Play only to climb without the above, and you will not improve, and likely won't climb either.
You need to learn why you aren't improving and climbing before you can start doing either.
Just start to recognize in what situations you die the most or kill the most. What are YOUR strengths, not what strengths you think you should have because someone told you to have those strengths. What champs fit your playstyle, don't just play what some pro is playing or some "good at ranked" player said was "op".
This is pretty basic advice that not enough people realize is pretty much the biggest reason people do and do not climb. Sure there are more specific things to learn, like ward placement and better mechanical play (like cs'ing), but you don't need to be a a Diamond 1 to understand it, you just have to be willing to understand and do it.
:) Hope that helps a little?