Before attempting to find the dalmations you are missing, make sure you have acquired Yellow Trinity & have beaten your first trip to Hallow Bastion, as these are requirements for the last few.
How to unlock yellow trinity:
There are 99 puppies found in chests, then the 2 parent puppies that can be visited in their house in 2nd District of Traverse Town.
I am going to list the Dalmations in the order they appear in the journal, which will make them not go in order by world. I feel like this will make it easier to track down those you are missing, as you will have naturally found several in your completion of each world.
1 - 30
1, 2, 3 - Traverse Town - Merlin's House. Glide to the island across from the house.
4, 5, 6 - Traverse Town - District 1, Alley - Use the Red Trinity spot to get to this chest.
7, 8, 9 - Traverse Town - Item Workshop, above Accessory Shop - open by using Green Trinity
10, 11, 12 - Traverse Town - In the secret Waterway
13, 14, 15 - Wonderland - On a platform in the Queen's Castle. Can be reached via high jump or through a secret passage in the forest
16, 17, 18 - Wonderland - Lotus Forest, on a high platform
19, 20, 21 - Wonderland - Tea Party Garden. High jump is needed to get up to this chest.
22, 23, 24 - Olympus Colosseum - Use the Blue Trinity to the right of the gate
25, 26, 27 - Deep Jungle - On the far end of Hippo Lagoon
28, 29, 30 - Deep Jungle - Vines 2 area, swing to this platform
31 - 60
31, 32, 33 - Deep Jungle - Waterfall Cavern, in one of these chests
34, 35, 36 - Deep Jungle - Blue Trinity in the camp area, near exit to Hippo's Lagoon
37, 38, 39 - Agrabah - Treasure Room of Cave of Wonders
40, 41, 42 - Halloweentown - Bridge area, just before entrance to Oogie's Manor. **Note** if you already finished Halloweentown, this will instead be in the center area of Manor Ruins
43, 44, 45 - Neverland, Top deck of the ship (where you fought Captain Hook) - use the white trinity by the captain's wheel to get this.
46, 47, 48 - Agrabah - hidden room in the Cave of Wonders (down bottom, waterways)
49, 50, 51 - Agrabah - Entrance to Cave of Wonders
52, 53, 54 - Agrabah - Chest in the Palace Gates area
55, 56, 57 - Monstro - Chamber 3
58, 59, 60 - Wonderland. Use the entrance to the Bizarre Room located above the Tea Party Garden. In here, you must kill all the heartless & turn on the lights. This will make a painting appear. Once you enter the painting, use lighting on the archway made up of red flowers for this chest to appear.
61 - 99
61, 62, 63 - Hollow Bastion - Grand hall (where you fight Riku the 2nd time) - when you go in, it will be on the left as you go up the curled staircase to where you fought Riku.
64, 65, 66 - Halloweentown - Go to moonlight hill (curly bridge) and take the Christmas Tree door by the base of the bridge. The puppies are in one of the chests in this small area.
67, 78, 69 - HalloweenTown - Moonlight Hill's white trinity
70, 71, 72 - Halloweentown - Guillotine Square - there is a toothy gray pumpkin on the left side of this area. You will need to climb one of the ledges to the right and glide over.
73, 74, 75 - Monstro - Mouth, on top of a stack of wood
76, 77, 78 - Monstro - Chamber 6
79, 80, 81 - Monstro - Chamber 5
82, 83, 84 - Neverland - Ship's Hold - fly to the top of the rafters to find this chest hidden there
85, 86, 87 - Neverland - Ships Hold - Use the Yellow Trinity to open a door, chest is in the room you unlock.
88, 89, 90 - Neverland - Captain's Cabin, after the fight with Shadow Sora.
91, 92, 93 - Hollow Bastion - bottom of Rising Falls (take a bubble to get to this chest)
94, 95, 96 - Hollow Bastion - Castle Gates, cast Gravity on the floating earth mound to bring this chest down to you
97, 98, 99 - Hollow Bastion - Library - After you finish the book puzzle, go in the door that opens by the save spot. Cast gravity on the floating earth mound here to bring a chest down to you.
The achievement will unlock as soon as you open the last chest. Don't forget to go visit the Dalmatian House in 2nd District of Traverse town to get some rewards:
12 puppies: Curaga-G Gummi Block
21 puppies: Firaga-G Gummi Block
30 puppies: Thundara-G Gummi Block
42 puppies: Mythril Shard
51 puppies: Torn Page, Mythril
60 puppies: Megalixir
72 puppies: Orichalcum
81 puppies: Ultima-G Gummi Block
90 puppies: Tech up
99 puppies: One of every Gummi, and an improved Aero spell
If you need any help, please ask in the comments and I'll be sure to give you a hand!