My friend had an external drive with NTFS format. She started using iOS, so she formatted it to HFS+ using iOS Disk Utilities. She had realized her mistake and unplugged the drive just after formatting. My question is if it is possible to restore at least part of this removed data? If so, what softwware do you recommend? Should I format this drive again to NTFS format before trying to restore it?
No. You're data is well and truly gone. The reformat will have removed all the file tables so that while the data may well be on the drive blocks there is no way of knowing what block belongs to what file, what the files were called and what the directory tree might look like.
Sorry for the bad news.
I've succeeded with this recovery - I've left this partition as is, bought and used easeUS recovery tool. I've tried with free ones, but all failed.