Yes, it is correct. But if I wrote this advertisment, I would say " ไม่จำกัดวุฒิการศึกษา" . This phrase is for writing. In my opinion , it is " No requirement for educational qualifications" The meaning of วุฒิการศึกษาไม่จำเป็น is also right but we never use in advertisment writing or formal writing. You can use it when you talk to someone. For example, your friend ask you that ตำแหน่งนี้ต้องมีวุฒิการศึกษาขั้นต่ำไหม?( Does this position need the minimum educational qualifications ? ) You can answer him "ไม่จำเป็น" ( it is not necessary )

As stated in above answer, "วุฒิการศึกษาไม่จำเป็น" can be heard in spoken language. But that statement also mean 'study or knowledge is not necessary'. We (native language) rarely use that statement; this one is preferable: 'ไม่จำกัดวุฒิการศึกษา' or 'วุฒิการศึกษาไม่จำกัด'