Here some ways to increase your score. Please feel free to post more tips in this thread!
Comeback Victory 2,500 Win a duel when your life points are lower than that of your opponent and the difference is 2,000 or more.
LP on the Brink 1,000 Win a duel when you life point is 100 or less.
Low LP 500 Win a duel when you life points is 500 or less.
Cards on the Brink 500 Win a duel when the number of cards in your deck is 0.
Few Cards 200 Win a duel when the number of cards in your deck is 5 or less.
Victory by Effect Damage Only 1,000 Reduce the opponent's life points to 0 by only effect damage.
No Damage Taken 500 Win a duel without receiving damage.
Over 3000 Damage! 500 Decrease the opponent's life points by 3,000 or more with one attack.
Over 5000 Damage! 1800 Decrease the opponent's life points by 5,000 or more with one attack.
Over 9999 Damage ! 3,000 Decrease the opponent's life points by 9,999 with one attack.
Perform a Tribute Summon 300 Conduct at least one tribute summon.
Perform a Ritual Summon 400 Conduct at least one ritual summon.
Perform a Fusion Summon 400 Conduct at least one Fusion Summon.
Activate a Spell 100 Use at least one Spell card.
Activate a Trap 100 Use at least one Trap card.
Comeback Victory 2,500 Win a duel when your life points are lower than that of your opponent and the difference is 2,000 or more.
LP on the Brink 1,000 Win a duel when you life point is 100 or less.
Low LP 500 Win a duel when you life points is 500 or less.
Cards on the Brink 500 Win a duel when the number of cards in your deck is 0.
Few Cards 200 Win a duel when the number of cards in your deck is 5 or less.
Victory by Effect Damage Only 1,000 Reduce the opponent's life points to 0 by only effect damage.
No Damage Taken 500 Win a duel without receiving damage.
Over 3000 Damage! 500 Decrease the opponent's life points by 3,000 or more with one attack.
Over 5000 Damage! 1800 Decrease the opponent's life points by 5,000 or more with one attack.
Over 9999 Damage ! 3,000 Decrease the opponent's life points by 9,999 with one attack.
Perform a Tribute Summon 300 Conduct at least one tribute summon.
Perform a Ritual Summon 400 Conduct at least one ritual summon.
Perform a Fusion Summon 400 Conduct at least one Fusion Summon.
Activate a Spell 100 Use at least one Spell card.
Activate a Trap 100 Use at least one Trap card.
