'Better' is kind of vague unless you specify a particular thing. We would probably talk about 'productivity or success' in regard to work/school or 'personal development or growth' in a more general sense. Or 'accomplishment' might be used, also. 'Improving' could also be used, although it is kind of vague. 'I hope my 20th year is productive.' 'I hope to accomplish a lot in my 20th year.' 'I hope my 20th year is one marked by growth and personal development.'

I think you mean: I hope to get better when I turn 20. Cheers, Diana

I do not know what it means. Do you mean you hope to get better... during your 20th year (between age 20 and age 21)? during your twenties (between 20 and 30)? by the time you reach the age of 20? on your 20th birthday?

it is ok but it's weird. why not just leave out your age?