Which is the most critical situation of Server which is very critical to handle or challenging for an Admin?

To reduce the downtime and unexpected hardware failures during the startup of server

Unexpected downtime and hardware failures are the most critical situations for a Network Admin

At the Time of updating the server we have to reduce the downtime of the server.Its done when any malfunctions are associated with our hardware components

updates downloaded and then we need to restart the server without downtime.

you have a critical updates downloaded & you need to restart the server without downtime.

It happens when any hardware associated with your server malfunctions. So that you will need a downtime depending on the type of hardware you want to get replaced. You will have to plan accordingly like whats the least minimum time to get back online properly and how to decrease the catastrophe caused during the downtime through proper load balancing or mirroring.