There is a badge for this as well
Start at Tinkerbell in CottonPuff - play her Tink Toss game there get 10,000 points see Tink again then
2nd go see Silvermist at Dewdrop Vale and then play Fish Bounce for 10,000 points (I'm stuck at 9,020 points
)
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however, I went back to Silvermist to see what I needed to do for sure and it allowed me to go to the next game in this quest so give it a try even if you don't get the 10,000 3rd go Neverberry Thicket and 10,000 in SpiderWeb game - return to silvermist when done.
4th go to Sunflower Gully and see Iridessa who sends you to get 10,000 in Firefly Game in Springtime Orchard - Return to Iridessa. she sends you to:
5th Rosetta's Garden in CherryBlossom Heights to catch FlowerPetal Game 10,000 points - return to Rosetta.
6th see Fawn at Maple Tree Hill - sends you to play Knothole Pantry Game 10,000 in Pumpkin Patch and then return to Fawn - she sends you to Tink
7th- Tink sends you to Evergreen Overlook to play the Snowflake game 10,000. Return to Tink who then awards you the Great Games Days badge.
Most of the games I scored over 10,000 points except for the Fish Bounce which was 9,020 - and it still allowed me to continue and earn the badge. Also, most of the games I quit after I scored a little over 10,000 (my hand hurts
hehe