There is no time limit vs monster/quest…
I didn’t do the last stage in the first Trials of Fortitude as I had not pass the level requirement at that time. This is my team in the first Trials of Fortitude:
Now I had Boril 3/60 and a maxed Kailani so I don’t use those 2* heroes. I try to kill Horghal with riposte but I make some blunders by not healing my heroes with some red potions and accidently using Spirit Link (doesn’t work well with riposte). Horghal’s skill almost kill my entire team save Boril… 
In the end, my true heroes save me: 
Carpet Bombing for life!