To get the certain monsters you want (such as Holy Doll or Kuriboh), all keep selecting "New Game" at the title screen. Every time you start a new game, you get randomized dice. If you are unhappy with what you got, do it again until you get the desired combination of monsters.
New tournaments
To get a new set of tournaments, win the first tournaments and the World Champ Cup.
Defeating Marik
Try for your level one monsters first. He usually goes first for Blue Eyes Ultimate, Black Skull Dragon, or a level 4 Treasure Chest which destroys every monster in the dungeon.
Easy wins
Save you strongest monsters such as Harpie Lady Sisters or Mystic Horseman by playing level 1 monsters to make a dungeon path. Then when your dungeon path is close to your opponent, try to summon your strongest monster. Have lots of movement, defense, and attack crests.
Good dice
Defeat Marik or Odion in free duels to get very good dice, such as Gemini Elf, Orgoth,and Metal Zoa.
Play the Paradox brothers a few times to get level 4 dice.
There are three tournaments in the game (Normal, Reverse and Dark). Win the championship in all three to unlock all except two of the dice in grandpa's store.
Warp Hole
Defeat Maxamillion Pegasus.
Summon Crest
If you need a Summon Crest, hold B to roll at least one. Note: This does not work on level 4 dice.
Red Eyes Black Metal Dragon
Defeat Joey in free duel.
Red Eyes Black Dragon
Defeat Joey in the world championship.
Orgoth The Relentless
Defeat Joey. Alternately, defeat Duke Devlin sixteen times in free duel.
Exploding Disc
Defeat Mokuba.
Crocozaurus
Defeat Joey in free duel.
Effective attacks
Some types are super-effective to others.
Dragon is good against Spellcaster
Warrior is good against Dragon
Beast is good against Warrior
Spellcaster is good against Zombie
Zombie is good against Beast
Symbols
You may have noticed that symbols may appear above a monster's level. There are three symbols:
Feather: Indicates that it is flying and can only be attacked by other flying monsters. It also can fly over other monsters, but unfortunately, other monsters can move under it. Monsters with this symbol use double the movement cost.
Tunnel: Indicates that it digs underground to move around, so it can move past other monsters.
Arrow: Indicates that this monster can attack a flying monster.