The only way to qualify is to check if you can find your main duties in such NOC codes description as:
0111, 0121, 1111, 1112, etc.
Some jobs can be really close to each other and often overlap in main duties, so if it is your case then try to adjust your reference letter so that it would better match one of the eligible occupations.
It is required that you indicate your Primary NOC code. Thus if you want to increase your chances to be within caps, you will have to split your package into two indipendent applications with different Primary NOC codes stated therein.
No you can't for that ineligible NOC (0122) but you can in another eligible NOC (0111, 0121, 1111, 1112, etc) provided as your education and work experience do not have to be in the same field. But you have to get your educational qualifications evaluated and also get references for your work experiences in CIC format.