Question about dual boot

"I just wanted to know the method used by the malware" - this question is really impossible to answer without identifying the malware.

Malware is just malicious software. That's an extremely broad classification.

Theoretically someone could write malware for Windows that can read and write to ext4 and looks for an unencrypted Linux file system so that it can make malicious changes, but this is very unlikely. Malicious software is generally targeted at the widest audience, and this scenario is far from that.

That being said, if you know that your system has been infected with malware, the only truly safe thing to do is to wipe all hard drives and attached storage, reinstall operating systems, and restore from backups that were taken and segregated prior to your device being compromised.