Warning! I think some would consider the video somewhat as a spoiler. The three monsters at the end of the wave 30 are the last ones you need to fight and stop them from getting the crystals. I had just barely made it with only one left at the end of the wave. It can sure be hard to win in your first try.
The key strategy here was to collect as much gil as possible for upgrades to your army. Using the thief is quite handy, because he can increase the amount obtained after you defeat an enemy.
Attacking units can also benefit from the colored crystals: the red increase attack power to units, the yellow increase speed power to units, and blue increase range power to units. Just make sure you place the crystal near the units for them to take affect.
I only played the one player mode, but there are more modes to choose from. Replay (as seen here) will show you the whole battle from the waves you have survived. Overall this is a very addicting, and fun game, I highly recommend it!