Stamps - Successfully complete the indicated task to unlock the corresponding stamp:

Dig Dug

Carrot: Grab the Carrot.
Complete Dig: Successfully dig the entire level.
Cucumber: Grab the Cucumber.
Eggplant: Grab the Eggplant.
Green Pepper: Grab the Green Pepper.
Mushroom: Grab the Mushroom.
No Dig: Successfully complete the level without digging.
Pineapple: Grab the Pineapple.
Quad Squash: Successfully squash 4 enemies with one rock.
Tomato: Grab the Tomato.
Turnip: Grab the Turnip.
Watermelon: Grab the Watermelon.

Dragon Spirit

Earthquake: Collect the Earthquake power-up.
Endurance: Successfully survive against a boss under a timed limit without killing him.
Fire Breath: Collect the Fire Breath power-up.
Homing Fire: Collect the Homing Fire power-up.
Incubation: Collect the Incubation power-up.
Maximum: Successfully get 3 heads and 6 fire power orbs without getting hit.
Over The Jungle: Get to the Jungle Area.
Power Down: Collect the Power Down power-up.
Power Wing: Collect the Power Wing power-up.
Small Dragon: Collect the Small Dragon power-up.
Small N Wide: Collect the Small Dragon, followed by Wide Fire without getting hit.
Wide Fire: Collect the Wide Fire power-up.

Galaga

Blue Spaceship: Destroy the Blue Spaceship.
Boss Alien: Destroy the Boss Alien.
Destroy Fighter: Successfully destroy your captured ship.
Dragonfly: Destroy the Dragonfly.
Dual Fighter: Successfully destroy the enemy holding your ship captive.
Maple: Destroy the Maple.
Perfect: Win a perfect game in the Challenging Stage.
Scorpion: Destroy the Scorpion.
Stage 10: Reach Stage 10.
Stage 20: Reach Stage 20.
Stage 30: Reach Stage 30.
Stingray: Destroy the Stingray.

Pac-Man

1600: Eat all the ghost after eating a single Power Pellet.
1600X2: Do the above task twice in one round.
Apple: Eat the Apple that appears in Round 5 or 6.
Bell: Eat the Bell that appears in Round 11 or 12.
Big Eater: Successfully complete Round 21.
Cherry: Eat the Cherry that appears in Round 1.
Galboss: Eat the Galboss that appears in Round 9 or 10.
Intermediate: Successfully complete Round 5.
Key: Eat the Key that appears after Round 13.
Melon: Eat the Melon that appears in Round 7 or 8.
Orange: Eat the Orange that appears in Round 3 or 4.
Strawberry: Eat the Strawberry that appears in Round 2.

Trophies - Successfully complete one of the following tasks to get a trophy:

Pac-Man Rookie (Bronze): Obtained four Pac-Man stamps.
Galaga Rookie (Bronze): Obtained four Galaga stamps.
Dig Dug Rookie (Bronze): Obtained four Dig Dug stamps.
Xevious Rookie (Bronze): Obtained four Xevious stamps.
Dragon Spirit Rookie (Bronze): Obtained four Dragon Spirit stamps.
Pac-Man Veteran (Silver): Obtained all Pac-Man stamps.
Galaga Veteran (Silver): Obtained all Galaga stamps.
Dig Dug Veteran (Silver): Obtained all Dig Dug stamps.
Xevious Veteran (Silver): Obtained all Xevious stamps.
Dragon Spirit Veteran (Silver): Obtained all Dragon Spirit stamps.
Xevious Resurrection Veteran (Gold): Obtained all Xevious Resurrection stamps.

Xevious

Ace Pilot: Destroy 500 air enemies in a single playthrough.
Andor Genesis: See Andor Genesis at end of Area 4.
Area 16: Reach Area 16.
Area 4: Reach Area 4.
Area 8: Reach Area 8.
Backfire: Destroy an enemy while another one is behind your ship.
Blaster Master: Destroy 100 ground enemies in a single playthrough.
Destroy Grobda: Destroy one of the tanks that moves when shot at.
Full Destruction: Destroy every part of the Andor Genesis before defeating it.
Sheonite: See Sheonite at the end of Area 9.
Sol Citadel: Find a Sol Citadel.
Special Flag: Find a special flag.

Xevious Resurrection

100 Items: Collect 100 shield items.
4 At Once: Successfully destroy 4 ground enemies with one bomb.
All Clear: Destroyed the Final Boss.
Boss 12 Clear: Destroyed the Level 12 Boss.
Boss 9 Clear: Destroyed the Level 9 Boss.
Enemy Collector: Successfully shot or bombed all enemies.
Free Play: Play Xevious Resurrection 50 times.
Laser Cancel 100: Used your shields against lasers 100 times.
No Shield Clear: Successfully clear a level without using your shields.
No Weapon Clear: Successfully clear a level without shooting and bombing.
Sol Discovered: Successfully found the hidden Sol Citadel.
SP Flag Found: Successfully found the hidden SP Flag.