This scripts remove old kernels and should keep the latest 2 kernels (or you can pass the flag --keep n to keep more)

purge-old-kernels

#!/bin/bash
# Install purge-old-kernels script for purging old kernels from apt-get
# This utility was extracted from bikeshed (sudo apt-get install bikeshed, http://packages.ubuntu.com/precise/misc/bikeshed)
FILE_NAME=purge-old-kernels
BIN_FOLDER=/usr/bin

echo -e '#!/bin/sh
#
#    purge-old-kernels - remove old kernel packages
#    Copyright (C) 2012 Dustin Kirkland <kirkland@ubuntu.com>
#
#    Authors: Dustin Kirkland <kirkland@ubuntu.com>
#             Kees Cook <kees@ubuntu.com>
#
#    This program is free software: you can redistribute it and/or modify
#    it under the terms of the GNU General Public License as published by
#    the Free Software Foundation, version 3 of the License.
#
#    This program is distributed in the hope that it will be useful,
#    but WITHOUT ANY WARRANTY; without even the implied warranty of
#    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#    GNU General Public License for more details.
#
#    You should have received a copy of the GNU General Public License
#    along with this program.  If not, see <http://www.gnu.org/licenses/>.

# Ensure we'"'"'re running as root
if [ "$(id -u)" != 0 ]; then
    echo "ERROR: This script must run as root.  Hint..." 1>&2
    echo "  sudo $0 $@" 1>&2
    exit 1
fi

# NOTE: This script will ALWAYS keep the currently running kernel
# NOTE: Default is to keep 2 more, user overrides with --keep N
KEEP=2
# NOTE: Any unrecognized option will be passed straight through to apt-get
APT_OPTS=
while [ ! -z "$1" ]; do
    case "$1" in
        --keep)
            # User specified the number of kernels to keep
            KEEP="$2"
            shift 2
        ;;
        *)
            APT_OPTS="$APT_OPTS $1"
            shift 1
        ;;
    esac
done

# Build our list of kernel packages to purge
CANDIDATES=$(ls -tr /boot/vmlinuz-* | head -n -${KEEP} | grep -v "$(uname -r)$" | cut -d- -f2- | awk '"'"'{print "linux-image-" $0 " linux-headers-" $0}'"'"' )
for c in $CANDIDATES; do
    dpkg-query -s "$c" >/dev/null 2>&1 && PURGE="$PURGE $c"
done

if [ -z "$PURGE" ]; then
    echo "No kernels are eligible for removal"
    exit 0
fi

apt-get $APT_OPTS remove --purge $PURGE' > "$FILE_NAME"

sudo chown root:root $FILE_NAME
sudo chmod 755 $FILE_NAME
sudo mv $FILE_NAME $BIN_FOLDER

Remote install

bash <(curl -s https://gist.githubusercontent.com/franciscocpg/ae1f5abb3e7be005b080/raw/)
and then
sudo purge-old-kernels