NTFS Hard disk about to die, I only have another ext4 hard disk and want to backup on it

According to your figures, the 1 TB drive that is failing has 330 GB free, which means that you likely have somewhere around 650 GB of data on it, and the 450 GB drive (I assume it isn't a 450 TB drive, or you likely would know better than to ask here) that you want to back up to now has 410 GB (also assumed unit) free.

Even if the best case, where you could use the whole 450 GB target drive to hold the files you want to back up, you would still be short about 200 GB on the target drive. And that's assuming that the files on the NTFS drive aren't compressed at the file system level, because ext4 doesn't support file system level compression.

Bottom line, by math you cannot fit all your data on the drive you want to back it up to and you haven't stated anything in the question that indicates that you want to selectively back up a smaller dataset.

If you care about this data, then I recommend that you go to a consumer electronics store and pick up an external drive and back up to that. A 1-2 TB external drive isn't very expensive these days, and it will be far easier, and likely faster in the end, than trying to at this point pick and choose which files to back up. A 2 TB drive will also give you a nice backup solution for future needs.

If you don't need a full backup and know what you'd want to back up, and that data will fit within the available free space, and you have stable NTFS read and ext4 read/write support, then I see no real reason why you couldn't do a backup by copying files by normal means. Depending on how the drive is failing and how far the damage has progressed, it's possible that some files may be damaged beyond repair and that you'd have to baby-sit the process, but I can see no technical reason why a normal copy couldn't possibly work.