Make a magical shirt without any seam or needlework
Find an acre of land between the salt water and the sea strand
Plow it with just a goat's horn, and sow it all over with one grain of corn
The main character must complete three impossible tasks or risk going mad as a result of a family curse.
Nancy Werlin wanted to see if she could write a book with a good-boy romantic interest, to contrast with the popular new bad-boy vampire romantic leads and unhealthy relationships she saw floating around in young adult fiction today. She writes more on her reasons for writing the story in the link below.
Hercules
That series of tasks was called the 12 labors of Hercules, and each one seemed impossible.
While some things may seem impossible, such as defying the laws of physics, it is important to remember that impossibility is often a matter of perspective and limitations. With determination, creativity, and innovation, many seemingly impossible tasks can be overcome or achieved.
Heracles, a demigod son of Zeus.
Humans cannot breathe under wayer or fly
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The question is impossible to answer. You clearly have some everyday tasks that you already have in mind and are looking for "other" tasks. Unfortunately, we have no way of knowing what tasks you do know of.
In one sense he was. He killed his wife, then was set 12 impossible tasks by Hera which he still managed to complete
A "herculean" task (after Hercules' 12 labors).
I think the greatest mythological greek hero would be Hercules because he did 12 almost impossible tasks.