If you move to Cyprus to work a regular job (employee), you may qualify for 50% reduction in taxable income, if your salary is at least 55,000 EUR/year. I don't know if this applies if you form a sole proprietorship. AFAIK, if you want to be self-employed, you also need to be an employer. That requires forming a company.
The advantage with salary is that you get access to the national healthcare system because you have to pay social insurance. It's not the best, but it's an option you'll have available to yourself.
The disadvantage is you have to pay social insurance and other payroll taxes. Those taxes are quite high.