The fastest and most direct way from Granada to Albufeira is by bus. There are no direct train services nor flights. Flights would mean Granada to Madrid to Lisbon to Faro and then bus/cab/transfer to Albufeira.
Unfortunately, the most direct daily service operated by alsa.es gets into Vale Paraiso/Ferreiras Bus Station at 02:30 in the night. It is unlikely there would be local buses or taxis to take you the 8kms to Albufeira at that time of night.
Consquently, you best option would be as follows:
1) Alsa.es - Granada to Seville (El Prado)
Dept: Arr:
Granada Seville
03:00 06:40
12:00 14:45
From El Prado Bus Station to Estacion Plaza das Armas I would recommend the C4 Bus in which runs from just after 6 in the morning till 23:30.
2) DAMAS/EVA Bus from Seville Plaza das Armas bus station to Albufeira Bus Station. (Daily)
Dept Arr
Seville Albufeira
07:30 10:00
16:15 19:40
You will have to buy two separate tickets for each sector as they are operated by different companies. Tickets for the Seville to Albufeira service cannot be bought online and can only be purchased in Seville so allow time to buy your ticket.