In story mode you can only gain one rank per game. Once you go up one rank (usually after reaching the goal within two minutes for a second time) just top out, watch the scenery change, and start again to gain another rank.
When a piece reaches the bottom, you can turn it indefinitely, giving you more time to think.
Skip levels in two player mode
To go to the next level, you have to win within the time limit. When you get to the point where you cannot win within that time, lose and you will play level one. Complete it, and you will be at a level higher from where you were previously. For example, if you are on level 8, lose and you will play level 1. When you complete level 1, you will then be on level 9.