After a monster is launched, it can trigger a Bump Combo if it collides with any of your other monsters. The monster who is bumped into will execute a bump combo, which can involve firing homing projectiles or shooting lasers, that can do a lot of damage.
Elements
Each monster belongs to a specific elemental type. Fire is stronger than Grass. Grass is stronger than Water. Water is stronger than Fire. Light and Dark are neutral to each other. Use this knowledge to construct a balanced party that can be strong against any type of opponent.
Expies
The Expie family of monsters resemble turtles. Instead of using them in battle, fuse them to other monsters to gain experience. Select the "More" option at the main menu to view the Expie Forecast. This will tell you where and when you can find a surge of Expies.
Friend Points
Take an online player's monster with you into battle, to earn Friend Points. They can be spent on the Hatcher.
Morlings
The Morling family of monsters have low stats. Instead of using them in battle, fuse them to other monsters to gain stat boosts.
Mormites (fire-type) give an attack boost.
Morquiks (water-type) give a speed boost.
Morlyfes (grass-type) give a health boost.
Shot types
Monsters have various shot types. Bounce-type monsters will bounce off anything they touch. Use them to make bank shots to start a combo on your other monsters. Pierce-type monsters pass through other objects, and will not change their trajectory. Use them to target weak points on Bosses.
Strike shots
Each monster has a strike shot that becomes available after a specific number of turns have elapsed during a battle. They are one-turn use special abilities that cause various effects, such as faster speed and increased damage. Once used, strike shots must recharge over time before they can be used again.