For this type of requirement, you can do a few things.
If using Campaign Responses then the field called Bounces will automatically come back into the custom field the integration creates called "Bounces" for all marketing automation solutions we support today.
If "Bounces" goes from 0 > 1 > 2 then you can assume it is a Hard Bounce from the Campaign History metrics.
MailChimp's API also supports mapping back "Hard Bounce" to Salesforce in Step 4 of your Sync Profile. Just use a simple CRM Checkbox field or Hard Bounce custom field to map from the MailChimp *Hard Bounce field.
Finally, if wanting to remove those in CRM which are bounced then run a report on the custom field "Hard Bounce" if using MailChimp to then remove those records from Salesforce.