Phantasy Star II
Guardians make their first and only appearance in Phantasy Star II. In the after biomonsters started appearing all over Mota, many rose up to combat them. These warriors were known as hunters. While most fought for good, some became rouge.
In order to fight this, a group called the Guardians were set up to police the hunters. These warriors were tasked with killing any hunter that strayed from the good path. The only known member of the Guardians is Anna.
Phantasy Star IV
Guardians are never seen or mentioned in Phantasy Star IV, and it's possible that hunters became able to police their ranks, making the Guardians unnecessary.
Phantasy Star Universe Series
A totally different group exists in this universe. Called GUARDIANS, it is a private security force tasked with assisting the Gurhal Police Force. They have been granted limited authority that can be overruled by someone of higher ranks, such as a soldier. The main goal of the GUARDIANS is to protect the innocent, though they can be hired for other tasks such as rescuing pets or settling fights.
The GUARDIANS main headquarters is a huge satellite, almost as big as the three planets. The 5th floor houses the official headquarters while the 1st floor has barracks for off-duty members. In-between is a huge mall. It also houses a training facility.
Becoming a GUARDIAN requires three months of training at the GUARDIAN Academy. The training basically entails protocol, combat training (mostly bladed weapons and guns), and a final exam. Completing Academy training does not automatically make one a full-fledged GUARDIAN. He or she must first spend time completing missions under the watch of a GUARDIAN trainer. Usually there is only one trainee to a trainer, though in times when GUARDIANS are short in hand it is permissible to take on two, as shown in the first game. Trainees are also given a robot helper to manage their schedule and store items.