Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Time Pressure; Situational Awareness; Workload; Distraction
Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Flight Deck / Cabin / Aircraft Event Illness / Injury; Inflight Event / Encounter CFTT / CFIT; Inflight Event / Encounter Unstabilized Approach
Air Traffic Control Issued Advisory / Alert; Flight Crew FLC complied w / Automation / Advisory; Flight Crew Returned To Clearance
Human Factors
En route from ZZZ1 to ZZZ2 we were directed by the physician on call to divert to ZZZ which we had just passed at FL350. The Captain gave me controls of the aircraft and radios and began the fix strategy. We were given a heading direct to ZZZ and began a descent to the airport. We began the approach on a visual right downwind as there was a cell to the north and west of the airport we wanted to avoid. Selected speed was chosen as we slowed down; however; when managed speed was selected the aircraft accelerated because I had not activated the approach. We captured the error; however; these few seconds caused us to be high and fast. Given the already high-altitude airport and compressed diversion time for the medical issue; we elected to do a visual left 360 and rejoin final. We had selected the final approach fix altitude; however; when we did our left 360 turn it took us away from the airport. The Tower Controller alerted us that he had an altitude alert and we climbed back to the 7;200 feet altitude for the fix we were now joining the ILS. We continued the approach without further issue.Cause - 1. Compressed; high pressure with the medical emergency of passenger with 60/40 blood pressure.2. Out of sequence normal approach and landing with the diversion that greatly compressed our time from top of descent to landing. 3. Choosing ZZZ - high altitude/high terrain as a divert airport.4. Loss of situational awareness as we made the turn away from the airport.Suggestions -1. Take vectors out for a longer final approach.2. If possible; choose diversion airports that have less threats. 3. If a turn for an airport is needed to descend or slow - make them towards the airport not away as altitude is less likely going to be an issue with regards to terrain avoidance.
During a medical divert we were high and fast.  On approach we accomplished a left 360 to descend.   We initially had 7;300 feet set and when we turned inbound and had the field insight we began a descent to 6;300 feet the final approach fix altitude.  Approach received a low altitude alert and informed us.  We climbed and continued the approach visually.  We never descended below 6;300 feet before the FAF.Visual approach; high and fast resulted in loss of situational awareness.  Avoid visual approaches when in unplanned situations; get vectors for an instrument approach.
Air Carrier flight crew reported receiving an altitude alert on approach to land. Returned to cleared altitude and continued on approach.