To monitor a cloud service such as Office 365, you need to know what technologies it's using and what workloads you're using in your solution.
To best accomplish the monitoring of your Office 365 solution, you will need to collect all the information about what workloads you are currently using, the environment technologies, architecture, and so on.
First, you need to make an inventory of your current environment, for example:
- Azure AD Connect
- Active Directory Federation Services (AD FS)
- Exchange hybrid
- SharePoint hybrid
- Skype for Business hybrid
- Office 365
- Any other services
In the case that you need to improve your monitoring solution beyond what is available out of the box, you may need to use third-party software to best monitor your Office 365 solution.
Microsoft also has other products that you can use to improve your monitoring solutions, for example...