Here is how assassin class can beat the time trial in the maze part of Refuge of Apostate.
Timing is crucial of pay close attention to the details of the video - it shows you exacly how to move. In fact timing is more important than speed because, as you will see, you can get sloppy and get frozen one or two time and still beat the clock. Getting burned by flame has no effect on your performance, but if you can't take so much damage then use dull pain to mitigate it.