The map is divided into 4 pieces
I'm going to call them left (L), middle (M), up (U) and right (R).
Here is a link to the complete map[imgur.com] with added circles for all items and people.

By following this path you should be easily able to get everything within the time limit (I had 7 minutes left).

Don't forget to pick up clocks for extra time and baseballs for Flam.
You don't have to go out of your way for them, just grab them when you're near them.

(U) Find the pink mushroom (near the entrance of the maze)
(U) Get the carrot (maze upper right corner) by finding the pink rabbit and answering Iran, China, Peter Rabbit.
(U) Get the gigacitron (above the maze)

(M) Get Violina’s pants (hidden in the mailbox next to the post office)

(R) Get the batteries (house with red roof and pool)
(R) Get Violina’s socks. (hidden in the bush behind the bikinis store)
(R) Buy 2 bananas from the clown (under the football field)
(R) Get the shell (beach on far left, right of the lighthouse)

(M) Get the matches (right bottom, next to a house with blue roof)
(M) Give the banana to the monkey.
(M) Give the broken helmet to the Fixit man.

(L) Give the fixed helmet back to Ukuleila.
(L) Show the pink mushroom to the guy with 3D glasses (next to the house with a pool)
(L) Get Violina’s shirt (hidden in the trash can, next to the bulletin board)

(M) Sell 1st picture (Ukuleila)
(M) Call 43893 and buy a drink from the Sober Up machine (next to Noodle Teaze)

(U) Give the chef the matches.
(U) Give Violina her clothes.
(U) Buy a daffodil from the florist.

(M) Give the daffodil to the woman with the yellow straw hat in her garden.
(M) Sell the 2nd picture (Violina)

(L) Use the shears to cut the fence.
(L) Enter the fence and get the screwdriver, alien picture and dumbbell.
(L) Go to the coffee shop (Sand Dollar cafe) to get a catalogue.
(L) Go to the coffee shop (Sand Dollar cafe) and choose: Golden Valley Bold Blend, small, 1 milk, no cream, 2 sugar and a pinch of cinnamon
(L) Give the hamburger to the diet guy.

(M) Give the dumbbell to Mr. Sala.
(M) Give the carrot, banana and kale to Cymbelle.

(R) Give the pink mushroom to Synthia.
(R) Talk the pervert guy with white t-shirt outside the bikinis store.
(R) Call 56172.
(R) Talk to Clef.
(R) Give the Sober Up drink to the drunk guy behind the Drunk Dragon/Island Ramen.

(U) Give the robot the screwdriver and batteries.
(U) Talk to the robot.
(U) Get the lighthouse key (far right of the beach above the city)
(U) Give the shell, gold coin and poster to Trompette.
(U) Give Xyla the alien photo.

(M) Sell 3rd, 4th, 5th and 6th pictures (Cymbelle, Synthia, Trompette, Xyla)
(M) Give Midi the catalogue.
(M) Buy Midi the video game.
(M) Open the lighthouse with the key and give the coffee to the guy inside.

(R) Give the dirty magazine to the pervert guy.
(R) Talk to Clef.

(M) Give Flam 20 baseballs.
(M) Give the lucky locket to Keytara.
(M) Sell 7th, 8th, 9th and 10th pictures (Midi, Clef, Flam, Keytara)