Short answer:
a. and b. are correct and very much likely, while c. is not.
Explanation:
There is difference in the three terms you so suggest. Going one at a time.
Over the past year, Nikodinov had been making eye-catching progress under the guidance of her coach, Yelena Tcherkasskaia, a former Bolshoi ballerina.
eye-catching - immediately appealing or noticeable; striking.
As the definition says, it is something immediately appealing. However, progress can't be really termed as striking at the first go. You can't really comment someone's progress to be eye-catching, since you have no idea whether they made any at all or not. It may happen that they were great from the very beginning. In that case, eye-catching skills would be the correct term. You can use this adjective with jewellery, posters, banners, etc., but not really with the progress of a person.
Over the past year, Nikodinov had been making noticeable progress under the guidance of her coach, Yelena Tcherkasskaia, a former Bolshoi ballerina.
noticeable - easily seen or noticed; clear or apparent or noteworthy
This, as the definition itself says, is clearly self-explanatory. The difference is, when saying this term we imply the hidden meaning that the person standing in front of us (the addresser) can themselves look how far she has come from where she was a year earlier.
We also get an alternative word from this, that is, noteworthy.
Over the past year, Nikodinov had been making noteworthy progress under the guidance of her coach, Yelena Tcherkasskaia, a former Bolshoi ballerina.
Over the past year, Nikodinov had been making considerable progress under the guidance of her coach, Yelena Tcherkasskaia, a former Bolshoi ballerina.
considerable - (of a person) having merit or distinction.
This would mean that her progress is worth rewarding, one that belongs to a distinction class.
Alternatives:
Over the past year, Nikodinov had been making significant progress under the guidance of her coach, Yelena Tcherkasskaia, a former Bolshoi ballerina.
Over the past year, Nikodinov had been making notable progress under the guidance of her coach, Yelena Tcherkasskaia, a former Bolshoi ballerina.
Over the past year, Nikodinov had been making remarkable progress under the guidance of her coach, Yelena Tcherkasskaia, a former Bolshoi ballerina.
Over the past year, Nikodinov had been making outstanding progress under the guidance of her coach, Yelena Tcherkasskaia, a former Bolshoi ballerina.
This might not be the best resource, but it may seldom be helpful for someone.
- noticeable vs considerable vs eye-catching
- significant vs remarkable vs notable vs outstanding