The most common and most likely answer to this crossword clue is the 8 letter word EYECHART
I've seen this crossword clue in Financial Times
E
Y
E
C
H
A
R
T
Buddy explains!
The straight part
We know that "One’s letters get harder to read" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one’s letters get harder to read = eyechart.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.