Learn English – Proverb for Someone will work, but another will get the benefit

For doing something that is too hard, or doing too much of it at one time, I'd say you could go with

Biting off more than he/she can chew

which usually implies "taking on too much/too may tasks", but I think it's fair to stretch it to "taking on a task that's too hard for you". This is, to me, the most obvious idiom for this, but it's fairly cliche.

You could also use

Getting in over his/her head (as in, the water is too deep)

which implies swimming somewhere where your feet can't reach the bottom, and yet you're not a strong enough swimmer to handle it. You can also use

He's out of his depth/He's in too deep

which is the same metaphor. Neither of these imply failure, since the speaker may have misjudged the swimmer/chewer. I can't think of a phrase that combines these with the notion that the task is impossible; usually impossible tasks are impossible for everyone and not just for one person (swimming in deep water may be impossible for him, in which case he's getting in over his head, but it's not impossible for me, in which case I just swim there).

Martin Manser, The Facts on File Dictionary of Proverbs (2002) offers two English sayings that are somewhat similar to the OP's in their view of the value of persistence:

constant dropping wears away a stone It is often possible to achieve a major purpose—for example, persuading people or breaking down their resistance—by a series of small but persistent actions or remarks: ... The proverb was first recorded in the 13th century, with different wording, but the sentiment it expresses is of ancient origin. Tibullus (c. 48–19 B.C.) "longa dies molli saxa peredit aqua {length of time eats away stones with soft water}."

and:

little strokes fell great oaks Great things can be achieved in small stages, or with persistent effort: ...The proverb is probably of ancient origin; in his Adagia (1500) the Dutch humanist Desiderius Erasmus quotes the Latinproverb "Multis ictibus deiicitur quercus {The oak is felled by many blows}."It also occurs in Shakespeare's play Henry VI, Part 3 (2:1): "And many strokes, though with a little axe,/Hews down and fells the hardest-timber'd oak."

The saying "Practice makes perfect" applies to persistence in developing mastery of some skill or task—which fits the situation of painstakingly gaining command of English—but it doesn't focus on persistence in working away at a task that is dauntingly large or otherwise difficult, and that doesn't show any meaningful progress after a even a fairly protracted amount of time dedicated to the task, as in the instance of sharpening steel into needles. For that scenario, I think, the two proverbs quoted in my answer are more suitable.