Symbols that appear over a monster's level have meaning:

• Feather - indicates that the monsters can fly and can only be attacked by other flying monsters. It can fly over other monsters, but monsters can also move under it. Flying monsters cost double in movement costs.
• Tunnel/Cave - indicates a monster that moves underground to move around. It can also move past other monsters.
• An Arrow - indicates that a monster can attack a flying monster.

Keep selecting New Game at the title screen until you get the desired dice/monsters you want.

Certain types work better against others. Here's a quick list of what's effective:

Beast is most effective against Warrior
Dragon is most effective against Spellcaster
Spellcaster is most effective against Zombie
Warrior is most effective against Dragon
Zombie is most effective against Beast