Identify achievements made by Islamic scholars during the Arab empire?

I assume you mean the Golden Islamic time from 8th to 13th century!

During this time, Islamic scholars were among the world's best. Among others they:

made achievements in maths (which is why algebra and algorithm are arabic words)

worked on scientific experiment as a technique to pursue knowledw

had some advancements in astrophysics (first reference to Andromeda Galaxy!

had a lot of advances in medicine, such as study of blood circulation, and of nervous system