Most of the movies can be unlocked by playing through PLUS mode, however the last few requires you to befriend with specific characters:

Effect - Code

Movie 20 - Max friendship with Kira and Athrun (Plus mode)
Movie 21 - Max friendship with Athrun, Rei, Heine, Lunamaria (Plus mode)
Movie 22 - Max friendship with Kira and Lacus (Plus mode)
Movie 23 - Max friendship with Athrun and Cagalli (Plus mode)
Movie 24 - Max friendship with Stellar (Plus mode)
Movie 25 - Max friendship with Stellar, Auel, Sting (Plus mode)
Movie 26 - Max friendship with Heine and Miguel (Plus mode)
Movie 27 - Max friendship with the 3 DOM Trooper Pilots (Plus mode)
Movie 28 - Max friendship with the 3 M1 Astray Pilots (Plus mode)