Have a look at this site which may assist:
http://www.solpraiaferias.com/index.php?content=cheg_en
Essentially it will be very difficult to get from Sevilla to Portimão on the afternoon ot 25th May.
There are two daily bus services from Sevilla Plaza das Armas bus station to the Western Algarve - Monday to Friday (only )operated by the Spanish company DAMAS.
Website: www.damas-sa.es
They leave Sevilla Plaza das Armas bus station
at 07:30 and 16:30 and take about four and a half hours to get to Portimão (for Praia da Rocha)
The problem is that Seville Airport is 15km from town and by the time you have collected your bags and got a taxi to Plaza das Armas it is unlikely you will make the bus. (Especially if the flight is late.)
Regretably there is no service on Saturday/Sunday.
The other options open to you are to hire a car its only 2 hours 15 minute drive motorway all the way.
Or take local buses to Ayamonte as previously suggested, ferry over the river and then train Vila Real Sta. Antonio to Portimao (see links on table above).
Finally the Spanish Bus Company Alsa.es operate a Service Sevilla - Lisbon via Faro. Unfortunately the services leave Seville at 15:00 and Midnight daily. If you caught the 15:00 on Saturday it gets to Faro at 16:30 local and you could then connect with a train from Faro at 17:31 to Portimão Station at 18:51. Taxi then to Praia Da Rocha.
The above links and info should enable to you to work out a return trip.
Hope this helps.
