This is a video guide giving the solutions of all the game levels. They may not be the most optimized solutions but they work and they are fast enough to get the time trials achievement.

About the time trials, there are no good advice i can give except to try remembering the most important steps in each solution when trying them. The first time trial is really short (2 minutes for the first ten levels) but all levels are short and straightforward. This is the one trial where you don't have much time to mess up. On the opposite side, in the other time trials you always have way more time than needed (Especially the last one that gives you 30 minutes for the last tem levels) so i'd suggest acting more carefully, especially since the levels become longer and longer and thus having to restart a level wastes a ton of time.