When hunting for Dalmatians, remember that some of them require abilities that the party hasn't acquired yet. The quest backtracks through areas like Traverse Town multiple times, so don't go crazy looking for Dalmatians that it seem to be impossible to reach. Chances are, the game will bring Sora back there with the tools necessary to grab those Dalmatians later on.

Traverse Town
1, 2, 3: The seemingly unreachable island across from Merlin's House. Come here after acquiring the Glide ability in Neverland, well into the game. Then it's easy to fly to the island.
4, 5, 6: Behind the Red Trinity in the District 1 alley. Come here after acquiring the Red Trinity ability, once all of the first ring of worlds is cleared.
7, 8, 9: In the Item Workshop, above Cid's Accessory Shop. Reach this by using the Green Trinity in the Shop.
10, 11, 12: Hidden in the Secret Waterway, again blocked by a Red Trinity.

Wonderland
13, 14, 15: On a high platform in the Queen's Castle, reachable via a hidden exit in the Lotus Forest -- above and to the right of the main entrance to the Forest.
16, 17, 18: On one of the high platforms in the Lotus Forest.
19, 20, 21: In the Tea Party Garden. Sora needs the High Jump ability to get here, so come back after completing the Monstro area.
58, 59, 60: In another nook in the Queen's Castle -- turn the faucet in the Bizarre Room and jump in the pot.

Olympus Colosseum
22, 23, 24: In the Blue Trinity to the right of the main gate.

Deep Jungle
25, 26, 27: On the far end of the Hippo Lagoon, easy to reach.
28, 29, 30: In the Vines 2 area, reachable by climbing the ivy in the Hippos' Lagoon and swinging over to the far platform.
31, 32, 33: In the Blue Trinity in the Climbing Trees area.
34, 35, 36: In the Blue Trinity in the Camp area.

Agrabah
37, 38, 39: In a chest in Aladdin's House.
46, 47, 48: On a high point in the Palace Gates area, reachable with the High Jump ability.
49, 50, 51: In the entrance area to the Cave of Wonders.
52, 53, 54: Accessible by bouncing up atop a treasure pile in the Treasure Room -- Aladdin must be in the party.

Halloweentown
40, 41, 42: In the Bridge area, just before the entrance to Oogie's Manor.
64, 65, 66: In a treasure chest in the Graveyard, which remains hidden until after Oogie is destroyed and Sora seals the Keyhole.
67, 68, 69: In Guillotine Square -- pull the bellrope at Jack's front door and look below the front stairs.
70, 71, 72: In Guillotine Square, atop the gray pumpkin. You need the Glide ability to float there.

Monstro
55, 56, 57: In Chamber 3.
73, 74, 75: Atop a stack of jetsam in the Mouth, reachable after the water level drops.
76, 77, 78: In another part of Chamber 3 -- try all the possible entrances.
79, 80, 81: In Chamber 5.

Neverland
43, 44, 45: In a corner of the Clock Tower.
82, 83, 84: On a beam in the Ship's Hold -- fly there after gaining the flight power.
85, 86, 87: Yellow Trinity in the Ship's Hold.
88, 89, 90: Chest in the Captain's Cabin, after Shadow Sora battle.

Hollow Bastion
61, 62, 63: In the Grand Hall, accessible the second time you visit here.
91, 92, 93: Bottom of the Rising Falls.
94, 95, 96: Castle Gates, cast Gravity on the floating chest.
97, 98, 99: High Tower, cast Gravity on the floating chest.

As the party gathers Dalmatians, go back to Pongo and Perdy's house in Traverse Town to periodically receive rewards. It's also cute to check out the Dalmatians at play, as the house gradually fills up. Here's the reward structure for snagging all the Dalmatians:

12 puppies: Curaga-G Gummi Block
21 puppies: Firaga-G Gummi Block
30 puppies: Thundara-G Gummi Block
42 puppies: Mythril Shard (weak!)
51 puppies: Torn Page, Mythril (sweet!)
60 puppies: Megalixir
72 puppies: Orichalcum
81 puppies: Ultima-G Gummi Block
90 puppies: Ribbon (what is this, Forgotten Worlds?)
9 puppies: One of every Gummi, and an improved Aero spell

When first entering a tournament, the whole party goes. After beating it the first time as a team, Sora can then enter solo, in either an ordinary progression or a high-speed time attack battle. All three of these methods net different prizes, so try all of them to rack up the most goods.

Here's the complete listing of tournaments and competitors (and since we're using the proper names for the monsters here, refer to the Monsters section to figure out what's what -- for example, a "Powerwild" is one of the Monkey Heartless from Deep Jungle).

Phil Cup
This is the first tournament, which begins after Sora locks the Traverse Town Keyhole.

1. 4 Powerwilds, 3 Soldiers
2. 1 Powerwild, 2 Green Requiems, 2 Red Nocturnes, 5 Yellow Operas
3. 1 Hammerlegs, 4 Powerwilds
4. 5 Red Nocturnes, 5 Yellow Operas
5. 1 Large Body, 5 Powerwilds
6. 1 Gauntlets, 3 Blue Rhapsodies, 4 Shadows
7. 2 Large Bodies, 6 Green Requiems
8. 1 Gauntlets, 1 Hammerlegs, 4 Powerwilds
9. 1 Armored Torso, 4 Yellow Operas, 4 Blue Rhapsodies.

Beat the Phil Cup to earn an upgrade to Sora's command of the Gravity spell.

Pegasus Cup
The second tournament is tougher, and features some familiar faces at the very end. This tournament becomes available after the party completes the Monstro area.

1. 2 Search Ghosts, 1 Bandit, 3 Air Soldiers
2. 4 Shadows, 3 Barrel Spiders, 2 Bandits
3. 2 Large Bodies, 1 Pot Spider, 1 Barrel Spider, 1 Fat Bandit
4. 5 Pot Spiders, 3 Yellow Operas, 2 Green Requiems
5. 4 Search Ghosts, 2 Fat Bandits
6. 3 Black Fungi
7. 5 Pot Spiders, 5 Barrel Spiders
8. 3 Fat Bandits, 3 Large Bodies
9. Leon and Yuffie

Yep, the bosses of this tournament are our friendly bounty hunters from Traverse Town. Yuffie is the one to smack first, since she possesses healing abilities, and the clever fighter can knock her shuriken back at her. Against Leon, get well out of the way when he charges up his Gunblade for a running slash. Victory earns the Strike Raid ability for Sora.

Hercules Cup
Finish out the second ring of areas, including sealing off Halloweentown and Neverland, to unlock the third Cup. This one is quite tough, and features the return of Cloud in the middle of the ladder. However, the party wins some great extras for completing this tournament.

1. 5 Gargoyles, 3 Shadows
2. 4 Wight Knights, 2 Barrel Spiders, 1 Air Pirate
3. 4 Pirates, 1 Battleship
4. 4 Gargoyles, 3 Wight Knights
5. 1 Rare Truffle (cast Gravity to beat him)
6. Cloud
7. 2 Air Pirates, 2 Pirates, 2 Gargoyles, 1 Wight Knight
8. 2 Pirates, 2 Battleships, 1 Air Pirate
9. Hercules

Hercules himself is pretty tough, although perhaps not quite as tough as Cloud, who is as annoying as Riku. Herc is invulnerable at times, though, while he's glowing yellow. To kill that invulnerability, bean him with a barrel (especially when he says "Hey, give up yet?" and poses), then attack while he's briefly vulnerable.

Finishing the Hercules Cup nets all kinds of stuff. Goofy gets Herc's Shield, Sora gets the Metal Chocobo keychain after beating Cloud and the Olympia keychain for finishing the first three tournaments, and beating the tournament also opens up the potential to use Yellow Trinity points. The first Yellow Trinity to hit is in the lobby of the Coliseum, where Sora can lock the Coliseum Keyhole.