On StackOverflow a question was asked about how to tweak and tune the performance of a Kohana-powered website. The result was a detailed answer from Pascal Martin that can be applied to just about any kind of web application out there, not just ones written in PHP.
Here are some points that come to my mind when talking about performances, scalability, PHP, ...First of all, there are many aspects/questions that are to consider : configuration of the server (both PHP, MySQL, and system) ; you might get more help about that on serverfault, I suppose, PHP code, database queries, using or not your webserver? Can you use any kind of caching mechanism ? Or do you need always more that up to date data on the website ?
He goes on to give tips about using a reverse proxy (like Varnish), using an opcode cache, caching data as well, profiling and optimizing SQL queries. He finishes it off with a more specific look at Kohana and how you can use some of its built in tools to accomplish these same goals.