The things I've thought of are not an average costumes.
Parappa: Three dimentional costume (he would be three dimentional like his anime). I'm not sure this one would be likely or easy to do.
Sackboy: Custom outfit (the outfit from your personal LBP account). This one's just a dream. The sackboy in PSASBR is different than the one in LBP so it wouldn't work.
Sackboy : Clive Handforth (LBP2)
Raiden: Frank Jager/Gray Fox/Cyborg Ninja (MGS1)
Spike: Jimmy (Ape Escape 2)
Mustachio Furioso (Tools Of Destruction, others) Just kidding, Deadlocked Armor (Deadlocked)
Drake: Wetsuit Drake (Drake's Fortune)
Sly: Pilot Suit (Sly 3)
Jak - Jak II Jak
Ratchet - Final Armor in Crank in Time (can't remember the name), Deadlocked Armor, Alpha Clank
Dante - Old Dante, Vergil (Maybe)
Heihachi - Soulcalibur II/Tekken 3 outfit
Drake - Suited Drake, Yemen Drake, Wetsuit Drake
Sackboy - Pretty much any customization pieces in LBP
Big Daddy - Subject Delta
Evil Cole - Vampire Cole
Sly - Tuxedo outfit, Samurai disguise
Emmett - Logan, Space Emmett (but there's not really much of a difference, so it might not be worth making)
PaRappa - It would have to be something based on another character. I have no clue.
Fat Princess - Blue Princess
Sweet Tooth- Twisted Metal 4 Sweet Tooth
Sly Cooper- Samurai Armor (scaled down a bit)
Big Daddy- Rumbler
Toro- Literal costumes, based on the actual characters represented
Jak- Jak 2
Raiden- Gray Fox
Evil Cole- Vampire
Sir Daniel- Gentleman/pimp
Kratos: His Leonidas preorder armour from GOW Ascension or one of his joke costumes.
Radec: Marksman Helghast or Winter helghast or (long shot) Sev.
Sly: Any one of his other ancestors, such as Ryachi or Sir Gallet.
Parappa: No idea.
Fatty P: No idea
Sweet Tooth: One of his older costumes from the earlier games.
Drake: Suited, heist, wetsuit or Golden Abyss look.
Big Daddy: Rumbler or Subject Delta
Toro: No idea.
Heihachi: No idea.
Jak: Prisoner threads
Good Cole: Kuo or Ice trooper
Ratchet and Clank: Final armour from Crack in Time, holoflux i think? Or any of his awesome armours.
Sackboy: Millions of possibilities, doesnt matter which one.
Dante: Old Dante i guess
Spike: No idea.
Sir Dan: VICTORIAN PIMP
Evil Cole: Nix or Militia.
Raiden: Gray Fox or MGS4 costume
Nariko: No idea.
Kat: Depending on what her alts are, any one that was missed out.
Emmett: Plated armour from multiplayer.