To unlock the Not On My Watch trophy in Battlefield V, you will need to revive 10 squad mates. The 10 revives required are cumulative and don't have to be obtained in a single match, so this trophy will likely be earned naturally.
The best way to unlock this trophy is to deploy as a Medic. You will automatically be put into a squad, or you can, of course, create your own squad. Simply stick close by to your squad mates and revive them whenever you have the opportunity.