How to get mount point of filesystem containing given file

On GNU/Linux, if you have GNU stat from coreutils 8.6 or above, you could do:

stat -c %m -- "$file"

Otherwise:

mount_point_of() {
  f=$(readlink -e -- "$1") &&
    until mountpoint -q -- "$f"; do
      f=${f%/*}; f=${f:-/}
    done &&
    printf '%s\n' "$f"
}

Your approach is valid but assumes the mount point doesn't contain space, %, newline or other non-printable characters, you can simplify it slightly with newer versions of GNU df (8.21 or above):

df --output=target FILE | tail -n +2

For Linux we have findmnt from util-linux exactly made for this

findmnt -n -o TARGET --target /path/to/FILE

Note that some kind of random mountpoint may be returned in case there are several bind mounts. Using df has the same problem.

You could do something like

df -P FILE | awk 'NR==2{print $NF}'

or even

df -P FILE | awk 'END{print $NF}'

Since awk splits on whitespace(s) by default, you don't need to specify the -F and you also don't need to trim the whitespace with tr. Finally, by specifying the line number of interest (NR==2) you can also do away with tail.