This is just a proof of concept, nowhere complete. I will probably implement this as its own Chrome extension and/or add it to Better TweetDeck.
It's a simple userscript that simply hides tweets, likes and retweets from "eggs" accounts on Twitter Web in your Notifications page. That's it. Install it and enjoy.
As said in the disclaimer, it's just a proof of concept. If proven actually useful/efficient it could be turned into a browser extension but will most likely be integrated into Better TweetDeck first.