I just unlocked Win 1st Hard without finishing the Uno Tournament on Normal. I finished it on Easy only. Here's what I did:
1. I unlocked everything on the game, all other 19 achievements, but after beating the tournament on easy I didn't want to have to play the tournament AGAIN on normal, so I let it sit.
2. When I got back to it seven months later, I saw I had a game going. At the time I wasn't sure what it was, but I assume now it was the last level of the easy tournament. I abandoned it and started a new tournament on normal.
3. Before playing a hand, I quit out of the game to the start screen.
4. Starting the game again, I chose to resume the game. I beat that level. I thought it was the first level of the normal tournament, but it appears to have been the last level of the easy tournament.
5. I don't know if I tricked the game somehow, but after beating that last level of whatever tournament I was on, I was able to start a hard quick play game.
6. Took three rounds to finish first in a hand, but the achievement popped.
Hopefully this will work for others who maybe have beat tournament on easy and don't want to start over on normal. It is worth a try anyways. It could save you a ton of time.