It took me about 90 minutes to complete the Trial of Hot Doom.
Ultimately I chose a Rose with a Speed Upgrade because she has a slower, longer jump but some people have also had luck with the Imp and his double jump ability.
Essentially the best advice I can give you is that you will first need to ignore the timer; paying attention to it at first will only add stress so ignore it until it's time to pay attention to it.
What you will need to do is concentrate on tackling each section in order to learn the proper jump timing and where you need to aim for your landing until you have done it so many times that you can sail right through it without hardly a thought or error. At this phase you aren't worried bout finishing, the timer or even getting to the next safe area- just concentrate on figuring out the correct timing for the next jump and the next landing point.
At no point should you pay attention to the timer or try to rush during this learning process- not even when you reach the final set of platforms.
Once you can reach the final safe area, where the "finish line" (or circle) is located, that is the point where you can start worrying about the timer. Once you know the proper sequence of timed jumps and landing points then you will need to work on dong it fast enough to make it to the end.
The key is to pick your character and to stick with it- if you change characters you may need to relearn the jump timing and landing locations all over again but the real key to avoiding frustration is to literally take it as the puzzle challenge it is and tackle it one jump at a time rather than looking ahead or watching the timer.