I'm using Ubuntu 12.04, and I'd like to know if I can replace the default login screen (Light-DM) for the one used on ELementary OS (Phantheon Greeter). If possible without installing the rest of the Elementary OS desktop.

Yes, you only need to Install pantheon-greeter and change the LightDM conf file like so:
To get pantheon-greeter you'll need to add this PPA, open a terminal and type:
sudo add-apt-repository ppa:elementary-os/daily && sudo apt-get update && sudo apt-get install pantheon-greeter elementary-theme fonts-open-sans-elementary fonts-raleway-elementary
gksu gedit /etc/lightdm/lightdm.confgreeter-session=pantheon-greetersudo apt-add-repository ppa:elementary-os/stable
Everyone is right but! Think it may be better to stay w/ Stable
Also try:
https://launchpad.net/~philip.scott/+archive/ubuntu/elementary-tweaks
This has bunch of tweaks under System Settings → Personal → Tweaks