This is the most direct route to Alcazaba (3371 m) when coming from Capileira (1436 m) and could be as short as the most straight route of the mountain, wich starts at Barrio Medio de Trevélez (1560 m). Usually there is no people doing the route from Hoya del Portillo (2150 m). You could find many people up to the point where the Mulhacen (3482 m) route joins Alacazaba's but you'll be almost alone from there to the summit and back to that point.
Hoya del Portillo (2150 m) is reachable on private vehicle from Capileira (1436 m) on a forest trail, wich is the continuation of the road A-395. In rain and snow seasons it could be difficult for a normal car.
From Hoya del Portillo (2150 m) turn to the left just after the parking barrier. The path ascend N wards in an afforestation pinewood. There are some zig-zags with easy short cuts so at 2280 m the trail must be taken to the left and reach a fire-lane. Ascend on it to Puerto Molina, where the path joins the forest trail wich starts at Capileira (1436 m) passing Hoya del Portillo (2150 m). Follow it N-NE wards leaving the Point 2622 and 2605 to the left and reach the point (2710 m approximately) where the forest trail joins Mulhacen and Alcazaba path. It's located to the N-NE of the rocks wich form Alto del Chorrillo (2721 m). 2h 20 min.
Ascend N wards from the Point 2710 along the long Loma del Tanto. The path traverse a wide trail in two occasions so at the third time (3020 m approx) it turns to the right (NE) leaving Tajos del Peñón Negro to the right. Follow ascending to approximately 3085 m, where the path starts a descent to Laguna Hondera (2850 m - 4 h 20 min). Surround this beautiful mountian lake on the SW shore and countinue NW wards to Laguna Altera drainage (3055 m approx) across Siete Lagunas basin.
Start the most difficult section of the route. It's a lose rock path wich closes to Peñón del Globo Occidental (3286 m) SW face leaving it to the right and ascending hardly to Peñón del Globo Occidental NW gap (3250 m approximately). Once there surround Meseta de las Borregas by turning to the left towards the Point 3307 first, then leave it to the left, pass to the right of the Point 3305. And finally ascend on the SW slope of Alcazaba (3371 m). 6h 15 min.
The descent is on the same route. Total time: 11 hours.
Junta de Andalucía has buses from Capileira (1436 m) to near Alto del Chorrillo (2700 approximately) and the other way round. So you could shorten the ascent of Alcazaba or the descent if you take the bus near Alto del Chorrillo.
More information on page 11 here (pdf).
In Summer take enough water with you and try to avoid July and August because of the heat. Do not forget a cap and a hard shell.
In late Autumn and Spring take crampons and ice axe if the route is snowed, the section near Peñón del Globo Occidental could be icy. If you don't want to take risks follow the trail from Laguna Hondera to Loma de la Alcazaba and up to the summit. It will add 55 minutes (Summer) to the route time.
Do not forget map, compass and altimeter whatever season you go.