Here is the full list of all 20 UNO achievements worth 200 gamerscore. It takes around 1-2 hours to unlock all of the achievements on Windows Phone.
1st win in a Hard round in Quick Play mode
Win 15th round in Tournament mode
Win 14th round in Tournament mode
Win 13th round in Tournament mode
1st win in a Normal round in Quick Play mode
1st win in an Easy round in Quick Play mode
Win 12th round in Tournament mode
Win 11th round in Tournament mode
Win 10th round in Tournament mode
Win 7th round in Tournament mode
Win 5th round in Tournament mode
Achieve the winner of 3 rounds in a row
When you draw a Reverse Card for the 1st time
Win 3rd round in Tournament mode
When you draw a Four card for the 1st time
When you called UNO twice for the first time
Make your opponent skipped for the 1st time
Win 1st round in Tournament mode
When you draw a Wild card for the 1st time
When you draw a Two card for the 1st time