Due to massive load increases on our website redis is now struggling with peak load because the redis server instance is reaching 100% CPU (on one of eight cores) resulting
The first thing to do would be to look at slowlog get 50 (or pick any number of rows) - this shows the last 50 commands that took non-trivial amounts of time. It could be that some of the things you are doing are simply taking too long. I get worried if I see anything in slowlog - I usually see items every few days. If you are seeing lots of items constantly, then: you need to investigate what you are actually doing on the server. One killer thing to never do is keys, but there are other things.
The next thing to do is: cache. Requests that get short-circuited before they hit the back end are free. We use redis extensively, but that doesn't mean we ignore local memory too.