Wondering if there is a way to see the CPU time used by a specific static class instantiated from a trigger handler. I see the overarching trigger cpu time used and then there is a dropdown that details method cpu time in dev console but feel like it isn't accurate. Whats whats the best way to see how much CPU time is used when a class or i guess more specifically a method is called
The easiest way to do this is to use the Developer Console, capturing the debug logs for a request that exercises your trigger and the related code then open the debug log and switch to the excellent Analysis perspective via the Debug menu's Switch Perspective option.
This allows you to drill down through the call flow and call stack and lets you see amount of time spent in your Apex code at aggregate or refined levels in that call flow/stack.
You probably will benefit from both examination of the Execution Tree view and the Performance Tree view. You may also like the Timeline in the Execution Overview.