UNO RUSH

I did this by setting up a house rules game where each player gets 13 cards and the game speed set to slow. Now just set up your cards on the left side of you hand in an order that you'll be able to get the 5 color changes. Now take all the cards on the right and move them to the left so you just have your run of color changes on top. Wait until you can play that first card and you'll get the achievement. You can also get the party planner achievement using this same method.

When your playing on slow you have a ton of time to move a card to the top so don't worry about not having the right card up there when it's your turn.

Use 6 cards of the same rank instead so you only have to shift the correct color to the front of your hand to get your run started.

Instead of the 1 in 10 chance of getting the correct top card on the discard pile, the first card you play will match the color of the discard pile and the following 5 cards will change the colors five times.