This quick guide will hopefully provide some hints as to how to better approach trial stages, as they are arguably a challenging part of the game.
As I saw nothing up yet, I threw this together to help players who are struggling with the trial modes in the game. The aim is to provide tools for the player to use, rather than just telling players what to do. If it seems necessary, I can add specific strategies for specific fields in spoilers.
What Can You Try Differently?
Start waves early. From what I've seen, spawns seem to be randomized (sometimes they come in clumps, sometimes spread out). If you know when there may be a gap with few monsters, spawn the next wave for some extra mana.
Combine/move gems around. Some may want to keep a gem in the back to clean up stragglers, but in reality this is wasted dps when there is nothing for it to shoot at. Move gems around to where they will have targets, and if towers are scarce, combine gems into a bigger gem and move that around, based on the spacing between clumps of monsters.
Look at your gems. They don't all share the same base stats. Does heavily relying on effects help get you further? Does combining those with the most damage output give you a gem than can hold out against the waves?
Look at the monsters' stats. Are they too much because of numbers (swarmlings), armor, or raw health? Do your two gems take 2.5 shots on average to kill each one? Does combining them make it take 1.25 shots on average instead(don't forget higher grades also shoot faster).
Look at the environment. Are there better terrain features you can take advantage of, that gives your gems more coverage(and thus time) to shoot? Are there beacons that are buffing the enemy, or shrines you could use at a better time? Is there some structure that the devs might have forced you to take advantage of for this map?
Don't be afraid to restart the level early. Sometimes 4 get through the third wave, and sometimes you get to the 8th wave with no problem. The biggest threat of monsters getting through, is actually slowing your progress and holding you back for the harder waves. Restart right away if it's clear you're going to be significantly set back in this try.
Finally, keep experimenting. I honestly doubt there is a strategy that works 100% of the time on every single map. Keep experimenting, and look at what approaches get you further, more often - and keep trying to refine them.