After completing the Main Story, you will unlock Mushroom Kingdom. Within one of the rooms inside Princess Peach's Castle, Toadette (known as Archivist Toadette this time around) can be found. By talking to Toadette, you will discover that she will be willing to give you a Power Moon for accomplishing a number of specific achievements (some of which you probably already done during the Main Story itself). In total, Toadette can award Mario with up to 61 Power Moons.
Toadette Power Moon Achievements
Rescue Princess Peach
Bring peace to all 14 Kingdoms in the world.
Collect 100 Power Moons.
Collect 300 Power Moons.
Collect 600 Power Moons.
Buy 13 things using regional Coins.
Collect 10 8-Bit Power Moons.
Collect 20 8-Bit Power Moons.
Collect Power Moons from 15 treasure chests.
Collect Power Moons from 25 treasure chests.
Collect Power Moons from taking Notes 5 times.
Collect Power Moons from taking Notes 20 times.
Collect Power Moons from Timer Challenges 10 times.
Collect Power Moons from Timer Challenges 25 times.
Meet up with Captain Toad 5 times.
Meet up with Captain Toad 10 times.
Meet up with Princess Peach as she travels the world 5 times.
Meet up with Princess Peach as she travels the world 10 times.
Herd sheep to collect a Power Moon 4 times.
Collect 5 Power Moons from Goombette.
Fish for Power Moons as Lakitu 3 times.
Grow seeds to collect Power Moons 5 times.
Grow seeds to collect Power Moons 10 times.
Catch 5 rabbits to collect Power Moons.
Catch 10 rabbits to collect Power Moons.
Dig up 15 Power Moons by Ground Pounding.
Dig up 45 Power Moons by Ground Pounding.
Collect 3 Power Moons by throwing your hat on things.
Collect 10 Power Moons by throwing your hat on things.
Collect 5 Power Moons from migrating birds.
Collect 3 Power Moons by wearing certain outfits.
Collect 8 Power Moons by wearing certain outfits.
Collect 15 Power Moons by wearing certain outfits.
Find 5 Bonneters hidden on people's heads.
Play the music that Toad wants to hear (5).
Collect 5 Power Moons using Hint Art.
Collect 15 Power Moons using Hint Art.
Collect 3 Power Moons playing Slots.
Win 10 Koopa Freerunning races.
Win 22 Koopa Freerunning races.
Receive passing scores in Koopa Trace-Walking (5).
Answer all of the Sphyx's questions correctly (3).
Collect 10 Souvenirs and stickers.
Collect 20 Souvenirs and stickers.
Collect 40 Souvenirs and stickers.
Capture 20 targets.
Capture 35 targets.
Capture 45 targets.
Collect 15 hats.
Collect 35 hats.
Collect 15 outfits.
Collect 35 outfits.
Open 14 Moon Rocks.
Travel through 10 warp holes.
Activate 40 Checkpoint flags.
Activate 80 Checkpoint flags.
Collect 1000 Coins.
Collect 5000 Coins.
Collect 10000 Coins.
Jump 10000 times.
Throw Cappy 5000 times.