Take a backup of the current sources.list, preferably make a full backup of the system.

Edit the sources.list file,
replace the occurrences of maya with nadia and precise with quantal.

$ vi /etc/sources.list

:%s/maya/nadia/g
:%s/precise/quantal/g

Resulting file may look like.

deb http://packages.linuxmint.com/ nadia main upstream import
deb http://archive.ubuntu.com/ubuntu/ quantal main restricted universe multiverse
deb http://archive.ubuntu.com/ubuntu/ quantal-updates main restricted universe multiverse
deb http://security.ubuntu.com/ubuntu/ quantal-security main restricted universe multiverse
deb http://archive.canonical.com/ubuntu/ quantal partner
deb http://packages.medibuntu.org/ quantal free non-free

Update the system

$ sudo apt-get update
$ sudo apt-get dist-upgrade