Indeed, GNU ddrescue is a good choice. Use it e.g. with 10 retries in case of errors:
ddrescue -r 10 -v /dev/faulty_drive /dev/external_drive optional_logfile.log
Note that by using the above command you are going to overwrite all data on your external hard drive.
Perhaps a safer way is to backup the data to an image file on your external hard drive instead:
ddrescue -r 10 -v /dev/faulty_drive /path/to/external/drive/image.file
For this you may need a file system on your external drive that supports file sizes of 2TB or more (e.g. ext2 and ext3 support file sizes up to 2TB whereas ext4, HFS+, or NTFS support even larger file sizes).
Example where /dev/sda is the faulty drive and /dev/sdb3 is the external partition (ext4) to write the image file to (run all commands as root):
mount /dev/sdb3 /mnt/external ddrescue -r 10 -v /dev/sda /mnt/external/faulty.img /mnt/external/rescue.log umount /mnt/external
Afterwards, if you want to mount specific partitions of your faulty hard drive image file faulty.img, you have to use corresponding mount offsets or tools like kpartx.
Another example taken from ddrescue infopages to rescue a whole disc /dev/hda to /dev/hdb:
First backup all error-free areas:
ddrescue -n /dev/hda /dev/hdb logfile Then try to recover any bad sectors:
ddrescue -dr3 /dev/hda /dev/hdb logfile