This is not really an easy one. I don't consider myself a terrible player and it still required an extra 30 seconds to get my mythical monster to evolve. I'd recommend getting the level 1 upgrade for the monster skills and then saving some gems for this.
Load up one of the later levels from an area of your choice and hope for a mythical monster. I did this in the forest area, where you have a 10% chance of encountering a mythic monster in the last area.
If it's not a mythical monster, you can right click and click the map at the top left to exit the round. Try again later or try another area which has a chance for mythical monsters.
Once you do get a mythical monster, choose the best monster you've gotten so far and do your best to score as high as possible. I believe you need around 2 million points to evolve an epic monster (this may vary in other zones, I've focused on the first one to unlock all the monsters there). If you run out of time, use some of your saved gems and keep at it. With an extra 30 seconds, most of you will get it. With an extra 60, everyone SHOULD be able to get it. The first extra time costs 10 gems, while the second costs 25.
Keep trying and good luck!