Complete Tutorial
All you have to do this this achievement is complete all 4 of the tutorial stages, these stages will teach you the basics of the game.

You shall not pass!
Fall more than 10 times on one level
You are able to obtain these as early as the first level, I am unsure if you can get this in the tutorial as I did not try. Now all you have to do to get it is fall of the platforms 10 times.

Ah gravity, thou art a heartless...!
Fall more than 15 times on one level
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Forest guard
Complete Fling Islands
You get this for completing all 8 stages in Flying Islands.

Bye, bye cowboy!
Complete Western
You get it for completing the 8 stages of Western.

Brrr, it's cold...
Complete Winter
You get it for completing the 8 sages of Winter.

Did you see Faith?
Complete Sci-Fi
You get it for completing the 8 stages of Sci-fi.

Young boy Scout!
Complete all levels
You should get this one at the same time as the Did you see Faith? Achievement, I do not know if the tutorial is included in this, but the DLC Christmas stages are not included.

Collect all umbrella at one level
The umbrellas are only of the Flying Island stages, on stage 1-4 you should just get the achievement anyway, as if you are not intentially trying to miss the umbrellas than you should normally pick up the two umbrellas on that stage and get the achievement.

Comlete level less than 10 seconds
The best level to do this achievement on is stage 3-4 as you can just jump of the beginning to the left and get to the end in a couple of seconds. It is achieveable on other levels like I got it on stage 1-2, but stage 3-4 is the best.

Don't fall after mine explosion
This can be done as early as the first level, most likely you will get this through progression of the game, but as a little tip try finding one with some room or something to stop you, and dont jump on the mine as that will send you flying.

Fall down after wind blow
This is done on Winter stages, and the wind looks like small clouds moving fast in certain locations, and all you have to do for the achievement is jump into one and it will do the rest.

Get killed by lazer
The lazers are produced by sentry looking machines that mostly have a red spotlight coming out of them, looking left and right, and to get them to use the lazer you just need to go into the spotlightfield and get hit by it for the ahcievement.