Fulfill normally has the connotation of 'all', so leave 'all' out. I think criteria is better. Requirements has a very slightly different connotation. Criteria is more about something you can put on paper. 'Requirements' might be something less tangible. But they can be used fairly interchangeably, on the whole.

"Requirements" is the correct choice. When a company announces a position they want to fill, they list the "requirements". Generally these specific experiences, education, and strong recommendations from people who know you. The company may also have criteria they use for making their choice but they are unlikely to let you know what those criteria are. Here are examples of criteria: "We need somebody who can do the job better than Mary" "We need somebody who seems modest or friendly or has a winning smile" "We need somebody who seems ambitious and smart" So, you see, criteria are scales of judgement, not specific facts that must be valid before you are allowed to apply.

I think both are fine. You can also use "satisfy" instead of "fulfil" if you want... just to give you even more choices!