NOTE: You don't have to get Power Berries in any sort of order. Feel free to pick them up at your lesiure, or even not at all if you want a challenge.
Power Berry #1
Attempt to chop down the cedar tree at the peak of Mother Hill.
It will ask you to not cut it down.
Select Don't cut it down to get the Power Berry.
Power Berry #2
Dig up tiles in the mine to find this Power Berry.
It can appear on any floor below the first one.
Power Berry #3
Donate 5 crops to the Harvest Goddess' pond, behind the waterfall.
You cannot donate crops after 6PM, nor on a festival day.
The Goddess will appear each time you donate a crop, and you'll be given the Power Berry on the fifth crop.
Power Berry #4
Find it behind the Winter Mine, out on the ice.
This Power Berry isn't visible; you have to just attempt to pick it up behind the mine.
Power Berry #5
Find it inside the Winter Mine, by digging it up.
As with the normal mine's Power Berry, it shows up on any floor from 2 downward, but not on the first.
Power Berry #6
Plant at least 91 flowers in your field.
You can do this in Spring, Summer, or Fall, it doesn't matter which season.
When Anna shows up, tell her she can have as many as she wants, and you'll get the Berry.
Power Berry #7
Trade it for 1001 medals at the Local Horse Race.
You can do this any year you want, and they don't have to be medals earned from racing on your own.
Once you have enough, just trade with the Mayor for the Berry.
Power Berry #8
Win the Opening Day swimming contest.
The key to winning the race is to press X every .3 seconds, or alternately, to use a turbo controller.
Upon winning, you get the Power Berry.
Power Berry #9
Fish it out of the ocean during Winter.
You can use either Fishing Rod or Pole for this, but the Pole is superior as usual.
Once you've fished the Berry up, that's all there is to it.
Power Berry #10
Buy it from TV Shopping.
It is the ninth item offered, after all the kitchen utensils are offered, and costs 5000G.
It will be delivered the next Tuesday or Wednesday (if Tuesday is a festival).
Mystic Berry - Aka. Kappa's Berry
Throw 3 Cucumbers into Mother Lake at the spot shown, facing away from the stump.
This can only be done in Spring, after 12:00PM, on a non-rainy non-festival day.
Kappa will appear each time you toss a Cucumber, and give you the Berry on the third one.