TOEM

As this game had been in PS for quite some time, hence there was a complete guide for this. you can refer below for all quests in Basto. Those quests with bracket are only available during certain period in the game. Credit to PSN Profiles for the guide.

Basto's Hidden Balloons
This is the "main" quest of Basto! You'll receive it automatically after talking to the Bus Stop NPC. Using your new Water Popper Attachment, pop 11 monkey-shaped balloons scattered around Basto.
1. In the second area with the jet-skiing Primitive Dude. Tied to a bush on an island behind the tower.
2. In the area with Nana's Tent, on an island with a waterfall and Beach Snakes popping up.
3. Take a nap to make it nighttime, then return to the jet-skiing Primitive Dudes. On top of a tower on the newly-accessible island.
4. In the area with the Cave, climb to the top of the area; on the cliff above the Cave's entrance.
5. After exiting the Cave, look at the water next to the hill with the hammock. If it's daytime, it'll look like it's floating in water. If it's nighttime, you'll see it's tied to the platform below.
6. After exiting the Cave area, walk behind some bamboo to find a water balloon target. Splash the target and hop in the open hatch. You'll be transported to a secret island. The balloon is out in the open.
7. In the area with Arthur the Unfinished T-rex (after the Cave exit), stand where you find an Eggert and look across the water.
8. In the area with the Castle, find the water balloon target and travel through the pipes to an island. Shoot the balloon that's floating lower than the main island's level.
9. In the area with the Castle, stand next to the Castle Guards and aim up at the nearby tower.
10. Inside the Castle, next to some sand castles.
11. Inside the Carnival Tent, next to a stack of boxes.

Take a Nap!
After reaching Nana's Tent, she'll recommend you take a nap. This is your introduction to Basto's new mechanic: Day and Night! Use any of the hammocks around Basto to take a nap and change the time of day.

Jet-Ski Tricks
Talk to the square Primitive Dude in the second area. He and his friend are looking for a rad photo of their jet-ski tricks. Go up to the edge, and aim your camera at the ramp. Wait until the jet-ski is mid-air to snap a photo. Return to the Primitive Dude and show him the photo.

Broken Dreams (Day Only)
There's a poor tiny Monkey sitting on a chair with a broken leg. Give them some Ice Cream, and they'll be miraculously cured! Don't forget to pick up the Foot Cast that they toss aside.

Dry Season
Standing next to a barren flower patch, a sad Farmer is having trouble growing flowers in Basto's terrible heat. Use the Water Popper Attachment twice to water the flower next to the NPC. Inspired, the Farmer realizes that water is crucial to grow plants. Water the rest of her dried-up flowers on Basto.
1. Next to the Farmer, in the empty flower patch. Required to start the quest.
2. Below where the farmer is standing, on top of a small hill.
3. In the area with Nana's Tent, on a small island.
4. Behind the Cave entrance, near the ladder to the nap hammock.
5. Inside the Cave, near the radio.
6. After exiting the cave, on a small hill next to a bike.
7. Inside the Castle, on the dining table.
8. Inside the Thirsty Fellow's house, from Dehydrated Muscles.
9. Next to the Bus Stop
10. Inside the Carnival Tent, on top of a box behind a chair.
11. In the area with Arthur and the big Bonfire, next to the ramp by the movie projector.

Dehydrated Muscles
In the area with the Cave, there's a Dehydrated Man huffing and puffing at the end of the pier. He'll give you an empty water bottle. Near the cave entrance, use the water pump to fill it up. Return to the Dehydrated Man and he'll be rejuvenated! Temporarily.
After he runs off, follow him and you'll find he's exhausted. Fill his water bottle again, and repeat this process a couple more times until he's finally returned home.

Book of Bats
Enter the cave and read the book on the table. The riddle inside tells you to honk at 3 sleeping bats while it's nighttime. Return to the book when you've woken all 3 sleeping bats.
1. In the first Cave room, same area as the book. Hanging from the ceiling.
2. In the area with Arthur, hanging from a string of lanterns.
3. In the area with the Castle, hanging by a tower with a painting easel on top.

Sweet Tooth
The Vampire released from the Book of Bats apparently has a sweet tooth for Ice Cream. Give him some.

Bitling Collector (Complete "In your face" & "Fruit shortage")
Near the Cave's exit, there's a pixel-faced Bitling Collector standing on a beach. Show him the photos of ALL Bitling creatures.
1. Bitling Frog: Daytime only. Sitting on a beach chair by the Carnival Tent.
2. Bitling Mouse: Inside the Castle, in front of a miniature version of the same Castle. Complete In Your Face to stop the Prince from getting in the way. (This will require you to complete Fruit Shortage to give him Ice Cream.)
3. Bitling Snail: Same area as the Collector, on top of a short bamboo stalk.
4. Bitling Tato: In the Bus Stop area, sitting on top of the spinning sign.

Arthur Hunter
An Archeologist is trying to find the remaining fossils of their magnificent t-rex, named Arthur. They will give you a Pickaxe to dig at "X" marks on the ground. When you've found a fossil, take a photo:
1. Femur: In the same area as Arthur, beneath the bridge to the Carnival.
2. Foot: In the Castle area, by the waterfall.
3. Skull: On the upper platform by the Bus Stop.

Night Lights (Day Only)
In the same area as Arthur, there's a small boy looking for a photo of a Fire Fly. You can only find them at night, flying in front of the Cave's entrance by the Ghost hangout. Since the boy is only available during the day, you will need to switch between Day and Night for this quest. Thankfully, there's a hammock in the same area as the boy.

Night-Time Cinema (Night Only)
In the same area as Arthur and the big bonfire, some creatures are trying to watch a movie. But, it's too bright! Splash and extinguish the 4 tiki torches near the movie screening.

Brain Freeze (Night Only)
In the same area as Arthur, there are arms flailing above an "X" on the ground when it's nighttime. Interact with the "X" to find it's a Viking Zombie in search of Ice Cream.

Spooky Stories (Night Only)
Next to the massive bonfire, there's a Camper trying to find a spooky tree to make their campfire story extra scary. Go to the area with the bamboo stalks and Bitling Collector. Behind some bamboo, there's a semi-hidden path to a water balloon target. Splash the target and jump into the open hatch.
You'll travel through pipes to a secret side area with a very spooky tree and one of Basto's Hidden Balloons. Take a photo of the tree and return to the Camper by the bonfire.

Bad Hair Day (Night Only)
Go to the area with Arthur the Unfinished T-rex. Take a nap and lower the water to reveal a mermaid! Only problem: she can't see with the seaweed in her face. Splash some water on her head. Now she can see her guitar!

Painterly Portrait
In front of the Castle, there's a Painter suffering from artist's block. Show her any of the "sparkle" portrait photos to get her inspired again!

In Your Face (Day Only)]/b]
Inside the Castle, there's a spoiled Prince who will antagonize you any time you attempt to take a photo. He promises to stop if you give him Ice Cream.

Fruit Shortage (Day Only)
Next to the castle, the Ice Cream Man is out of fruit. Around Basto, find 4 trees with special, non-coconut fruit. Splash at them to make the fruit fall. Bring all 4 fruit back and you'll receive Ice Cream in return.
1. Banakin: In the same area as the Castle, use the pipe hatch to travel to a side island.
2. Beanut: Outside Nana's Tent.
3. Melonpear: Near the hammock, in the area with the jet-skiing Primative Dudes.
4. Oranganas: Behind the movie screen, in the area with Arthur.

Sand Castle Competition (Day Only)
The King and Queen are having a sand castle competition! Inside the Castle, there are 6 sand castle entries on display. Take a photo of your 3 favorites. Take the photos to the frames behind the King and Queen, and place your #1 choice in the frame below the tallest column, #2 choice in the mid-height column frame, and your #3 choice in the shortest column frame. Take to the Queen to start the judging and complete the quest.

Play a Carnival Game (Day Only)
In the same area as Arthur and the big Bonfire, there's a bridge leading to a Carnival Tent. Play each game once, then talk to the Carnival Leader!