LAMP Stack and VPS Performance

Most of your CPU time is spent by PHP code, so you will need to start disabling all the plugins and modules and see if it makes a significant difference. If you can't, you need to profile the PHP code that is running and see what parts of the code are consuming most CPU and start there.

If you are not up to that, you need to weigh up the cost of hiring a PHP professional against the cost of renting a VPS server with more CPU power.