Walkthrough

1. To make Slowpoke yawn a 100-point yawn, you must first make the environment humid enough for it to feel drowsy.
2. Begin by using the Water Gun ability to moisten as many soil or grass tiles as possible. If you're running low on PP, have Leppa Berries or other food available!
3. Once you're done, check in with Slowpoke to find out that it's not enough for a 100-point yawn. It will then make a suggestion.
4. After Slowpoke's suggestion, search the map for low areas with nearby channels. These areas likely have clogged water sources.
5. Once you find the source, use Rock Smash to clear the clog and allow the water to fill the streams, ponds, and springs. A good example would be the area just behind the Pokémon Center, or the area near Drillbur's fields.
6. Speak to Slowpoke again after revitalizing the ponds to get another suggestion. Purchase Horsea fountains from the PC shop and set them up inside these ponds to have them spew water, making the surrounding air more humid.
7. If you lack the Life Coins to afford Horsea fountains, try completing the challenges in the PC!
8. If you find yourself watering everything for a while and Slowpoke is still stuck at 71 points, don't worry. Simply pull up the Requests menu and view the Yawn Up a Storm request details to find out which Pokemon to talk to and help next.
9. You must then fulfill the requests of these Pokemon to increase the environment's humidity. Read on to find out more!
10. Speak to Bulbasaur for another suggestion. They will tell you that fields of flowers increase the humidity in the air.
11. Purchase wildflower seeds from the shop and plant them close to each other, then bring along Bulbasaur to make them grow instantly!
12. Alternatively, you can use the Rototiller skill to pick up existing wildflower patches and place them right next to each other.
13. Another thing Bulbasaur will suggest is to revive 10 trees by using Water Gun on them, so gladly oblige and search for withered trees all over the map to spray on.
14. Speak to Squirtle next and they'll ask for a new habitat to live in: a hydrated tall grass habitat.
15. Spot a dip to the east of the map, a little way to the right of the workbench. The clogged water source is just above it, so smash the clog and fill the basin.
16. Then, use the Leafage skill to make tall grass grow all over the edge of the basin to create this habitat. Once you're done, bring Squirtle there and have them move in!
17. Moving into the hydrated tall grass will give Squirtle an idea. Speak to them to get the request of making a rain dance site which will involve two Castform Weather Charms, a wooden plate, and a food offering.
18. Pick a spot to set it up in, make it, then report back to Squirtle to start the rain dance.
19. You can purchase Castform Weather Charms from the PC shop, but you can also find them by exploring and finding treasures by diving into water ripples or digging for relics and loot.
20. However, the easiest and cheapest way to get them is by speaking to Professor Tangrowth, going back to his former home (your starting point), and rummaging through their items.
21. With all of these in place, it's time to speak to Slowpoke and see if you can get that 100-point yawn, which you will if you've done everything properly and gone out of your way to do more.
22. However, the rain will be short-lived, discouraging everyone. A loud roar will then be heard from the ocean up north, so go ahead and check it out.
23. Go to the fishing docks to the north of the map to find the legendary Pokemon, Kyogre, at the end of the broken docks.
24. Go to the nearby workbench, craft some bridge planks, and rebuild the docks to make your way to Kyogre. Speak to them about the rain, and they will agree to help you out.
25. After the cutscenes of everyone celebrating, return to the cave Onix is trapped in. Now, you can use Rock Smash to destroy the walls around them!
26. They will thank you for all that you've done, and ask you to thank the rest of the crew for their efforts as well. Return to everyone in front of the Pokémon Center to relay Onix's message, and this should conclude the request!

Walkthrough source: Game8.