Since installing 13.3 my Mac Book Air has slowed down considerably.

The obvious standout in the report is the CPU usage of Google Chrome Helper. There is lots of talk about that through web search, but don't know if that is the cause of your problem.

Does quitting TiVo Desktop that launches on startup make any difference?

There is a period of time after update that Spotlight could be indexing in the background, but I hadn't noticed that for more than a couple of hours.