If you tell me it needs to be fixed, I'll think it needs to be repaired. If you tell me it needs to be fixed up, I'll think it needs to be restored. That would mean things like new upholstery, new paint, etc.
When used in conjunction with a verb as a preposition or part of a phrasal verb, up (when it does not mean the opposite of down) often means "completely" or adds emphasis. (cf "Open the box." with "Open the box up" )
1. "Huh! It won't start! This car needs to be fixed." a small quantity of repairs are "fixed"
2. "Look at it! It is rusty, the door is falling off, a wheel is missing, there is only one seat, half the engine is missing; this car needs to be fixed up." - here fixed up = restored to a functioning and acceptable state.
Se also "to do up" = restore; "to close up" = shut securely; "freeze up" - to seize through cold; "to smarten up" = to tidy thoroughly; to top up = to fill to the brim; etc.