PA-28 Flight Instructor with student reported loss of electrical power and affected systems during approach. Flight crew continued and landed safely.

Narrative

During an Instrument Basic and Procedures flight with my student in Aircraft X we experienced a complete loss of electrical power. This happened approximately 2nm after crossing the IAF ZZZZZ for the RNAV XX into ZZZ at 2700 feet. Initially we only lost the ADC and AHRS (all traditional pitot static and gyroscopic instruments had the red 'X' indicating a failure) as well as both GNS430's which just went black. At this point in time when the GNS430's failed the system automatically reverted to guard and we lost the ability to adjust the flight plan; approach; and any frequencies. I also took flight controls and had the final say in all flight operations at this point in time. ZZZ Approach was listening on guard as well as we were helped relay information by another nearby aircraft. I told them we had experienced a failure on both of our GPS; as well as our flight instruments; and needed to receive clearance for a visual approach to runway XX at ZZZ. This was in VMC. I did not yet have the airport in sight so Approach issued me a heading and descend to 2000 which I flew using the magnetic compass and the standby instruments. Once I had the airport in sight I let them know and they cleared me for the visual approach. Almost instantly after receiving clearance for the visual approach for XX both the PFD and MFD went black and we lost all engine indications including fuel quantity and pressure and oil temperature and pressure. At this point in time I requested priority handling and squawked 7600 per the request of Approach on guard for lost comms. Upon requesting priority I ran through memory items such as cycling the battery master and altimeter as well as pressing the standby power button on the standby attitude indicator. There was no change. Also because I lost my engine gauges I enrichened the mixture and turned the electric fuel pump on. I realized that the electric fuel pump was most likely not working because of the loss of electrical power. However; I turned it on for the purpose of redundancy. At this point in time we were still able to transmit on guard even though the communication was very broken and static. ZZZ tower issued us a landing clearance for Runway XX #1. I read back the landing clearance and advised them that we would attempt to exit the runway at taxiway 1. We were able to exit on taxiway 1 and within 30 seconds all communication failed in the cockpit and with ATC. The transponder also failed with the annunciation 'XFAILX' before going dark. I held position once exiting the runway at taxiway 1 and waited for fire brigade and airport operations vehicles to escort. The fire chief came up to the aircraft and asked if we were okay to which I responded yes and then he told me that they would follow us to park at the academy ramp. I taxied and crossed runway XY to the flight school ramp. I shutdown the plane; advised my student not to answer any questions and immediately called school before talking to any airport personnel. Person A with flight ops advised me that I should talk to maintenance. At this point in time the airport operations personnel questioned me about the event. 'What failed for you to declare complete electrical failure'; 'which indications were lost'; 'was there trouble determining engine instrument indications' 'how much fuel was remaining'; they also asked me for my contact information. I then got ahold of my supervisor and asked for the maintenance phone number without relaying any other information other than the fact that both my student and myself were okay. I talked to Person B with the Flight Safety team and gave him an in depth recap of the events as well as answered all questions that he had for me. At the conclusion of our conversation he advised that I submit a maintenance and safety report. Both myself and the student were unharmed. I was able to make a safe and successful landing. The plane experienced no damage other than all aforementioned failures.