The question is simple and very green. How do I view other riders achevment badges and more detailed stats?
I do not believe there is a way to see other riders achievement badges.
As for “detailed stats”, that depends on your definition of “detailed stats”. You can get quite a bit of information via the Zwift Companion app. There is general information (e.g., mileage, gender, height, age, time in game, etc…) Also, there is a listing of their rides. You can select rides and view power, cadence, and HR.
If you want more detailed information or statistics, you would have to either look at that riders Strava or Zwiftpower account. There is no guarantee that they will have either one. Also, you would need to know what user account they are using on those services.