To unlock the Master of Time trophy in Mortal Kombat 11, you will need to complete 250 towers. You can simply quit out of the match once it starts to speed this up, although this should only be done once you have completed all of the other Tower trophies as they'll give you some progress towards doing this and cut out some of the grind.
You will also unlock the Tower Champion trophy once you compete 125 Towers:
From the Main Menu > Konquer > Klassic Towers > Endless
Start the Tower with whichever character you want (Scorpion is the quickest option). Once the Tower starts, press
and select Finish Tower.
Rinse and repeat until you unlock the trophy.