I think a guide needs to be started on these Webkinz Medallions! Until then, we can all post here! I will update as more users and I find out new information!
It's important to note that although you may get a 'great score', you may not get a prizebox (chance of getting a prizebox is about 1/3 games). Also, even if you do get a prize box, the chances of getting a medallion is quite low (about 1/6 will be a medallion, if not lower). Items from the floral theme and kinzcash are awarded more often then medallions unfortunately.
Addition: I have some real stats from an experiment I did with Polar Plunge and the minimum score needed to get a prizebox (see Polar Plunge section below for more information):
1. 20 games, I got 9 prizeboxes and 3 of them were medallions.
2. 20 games, I got 6 prizeboxes and 1 of them was a medallion
I was doing a lot of experimentation for a few arcade games to try and figure out the minimum score needed to earn one of those prize boxes! I have listed my findings below, and have included what other users have found as well!
I'm not sure this is true, but the minimum for each game might be different for everyone. I say this because some users have gotten prizeboxes after getting scores much lower than I have, yet I have never won a prizebox after getting those same lower scores. For example, for Polar Plunge, I cannot get a prizebox unless I get a minimum of 30 kinzcash, while some users have gotten prizeboxes after submitting lower scores. I play about 80 games of Polar Plunge a day, so although this has been tested, it is still not proven.
Ahem anyways, onto the scores...
Gummy Gumdrops:
It was hard to determine a score for this game because I found that the 'distance' was an inaccurate measure. Sometimes I got the prizebox at a distance of 19 000, but sometimes I didn't. I then switched to thinking that maybe the prizebox is related to the final score received. However, this was hard to determine because you are constantly collecting gumdrops faster than the score updates. Thus, I have used the amount of kinzcash earned as the benchmark.
70 Kinzcash is the minimumthat I have determined after extensive experimentation, but one user got a prizebox after 53 Kinzcash with a score 21329
Atlantiles:
One user got a prizebox at 38 kinzcash with a score of 7629
Polar Plunge:
I recommend that you play on medium difficulty: the score increases quite quickly (easy mode increases too slowly) and you don't have the difficulty of many drops and obstacles as you would in hard mode.
7500 points and 30 kinzcash is the minimum
Jumbleberry Blast
I finished the game with 30 716 and got a medallion, but I forgot how much kinzcash I earned so I'll keep this note here
One user got 75 kinzcash with a prizebox
Dogbeard's Gold
I got a prizebox at 55 kinzcash, but one user got a prizebox at 33 kinzcash
Crafty Canaries
Level 10 is what I have read so far from the posts in this thread, so we'll go with that for now
Cash Cow
One user got a prizebox with 45 kinzcash on regular mode
Leapin' Llama
17 kinzcash with a prizebox for one user
Zingoz Zangoz
I earned 24 kinzcash and didn't win anything
Hatch the Dragon
Eager Beaver Adventure Park
Ms. Cowoline's Rollcall
Hoppy Little Rocketship
Lily Padz 2: Downpours
Pet Party Parade
I will try to update if I find out new information. If anybody has any other information about these games, scores, or other games, feel free to post below! It's all about helping each other to try and get as many pet medallions as possible!
It's important to note that although you may get a 'great score', you may not get a prizebox (chance of getting a prizebox is about 1/3 games). Also, even if you do get a prize box, the chances of getting a medallion is quite low (about 1/6 will be a medallion, if not lower). Items from the floral theme and kinzcash are awarded more often then medallions unfortunately.
Addition: I have some real stats from an experiment I did with Polar Plunge and the minimum score needed to get a prizebox (see Polar Plunge section below for more information):
1. 20 games, I got 9 prizeboxes and 3 of them were medallions.
2. 20 games, I got 6 prizeboxes and 1 of them was a medallion
I was doing a lot of experimentation for a few arcade games to try and figure out the minimum score needed to earn one of those prize boxes! I have listed my findings below, and have included what other users have found as well!
I'm not sure this is true, but the minimum for each game might be different for everyone. I say this because some users have gotten prizeboxes after getting scores much lower than I have, yet I have never won a prizebox after getting those same lower scores. For example, for Polar Plunge, I cannot get a prizebox unless I get a minimum of 30 kinzcash, while some users have gotten prizeboxes after submitting lower scores. I play about 80 games of Polar Plunge a day, so although this has been tested, it is still not proven.
Ahem anyways, onto the scores...
Gummy Gumdrops:
It was hard to determine a score for this game because I found that the 'distance' was an inaccurate measure. Sometimes I got the prizebox at a distance of 19 000, but sometimes I didn't. I then switched to thinking that maybe the prizebox is related to the final score received. However, this was hard to determine because you are constantly collecting gumdrops faster than the score updates. Thus, I have used the amount of kinzcash earned as the benchmark.
70 Kinzcash is the minimumthat I have determined after extensive experimentation, but one user got a prizebox after 53 Kinzcash with a score 21329
Atlantiles:
One user got a prizebox at 38 kinzcash with a score of 7629
Polar Plunge:
I recommend that you play on medium difficulty: the score increases quite quickly (easy mode increases too slowly) and you don't have the difficulty of many drops and obstacles as you would in hard mode.
7500 points and 30 kinzcash is the minimum
Jumbleberry Blast
I finished the game with 30 716 and got a medallion, but I forgot how much kinzcash I earned so I'll keep this note here
One user got 75 kinzcash with a prizebox
Dogbeard's Gold
I got a prizebox at 55 kinzcash, but one user got a prizebox at 33 kinzcash
Crafty Canaries
Level 10 is what I have read so far from the posts in this thread, so we'll go with that for now
Cash Cow
One user got a prizebox with 45 kinzcash on regular mode
Leapin' Llama
17 kinzcash with a prizebox for one user
Zingoz Zangoz
I earned 24 kinzcash and didn't win anything
Hatch the Dragon
Eager Beaver Adventure Park
Ms. Cowoline's Rollcall
Hoppy Little Rocketship
Lily Padz 2: Downpours
Pet Party Parade
I will try to update if I find out new information. If anybody has any other information about these games, scores, or other games, feel free to post below! It's all about helping each other to try and get as many pet medallions as possible!

Webkinz World
.Pet Medallions are a whole new way to get more Webkinz pets, just by playing! Prize pools all around Webkinz World have been updated to include these medallions, including a new prize drop system in the Arcade! Track and manage your Pet Medallion collection in My Pets. 5,480 likes 219 talking about this. Shop for Webkinz Pets, Plush, eStore points and Deluxe Memberships. Dress up your pet and decorate your Webkinz World.