Is there a cut-off point where the lack of qualifications doesn't
matter anymore and experience/achievements can make up for that?
It depends on your field.
I don’t have a computer science degree, but for the past 2 decades I have managed to get computer gig after computer gig. First being an I.T. person. Then desktop publishing. Then web design. Then web development. Then Unix systems administration. Pretty much all self taught on the job as well as on my own. Now I have actually been tutoring & consulting with others. Showing them my skills. They have degrees & I don’t!
I have a steady job now & am respected for what I do. But there are times I wonder if I should get a grad school degree in something computer related because I feel I have to fight harder to get similar pay as my peers. And sometimes I wonder if I could work a fraction as much as others & earn more pay if I had a true comp-sci background.