Super Cloudbuilt

"Rush Mode" is a series of gauntlet challenges in which you are supposed to complete a predetermined set of levels with a limited amount of lives in the fastest time possible, then compete with other players online.

As far as trophies are concerned, only the Marathon sets are relevant. You will need to play "Complexity" first, which will unlock the "Core 16" set as well as Pheidippides, then you must play "Core 16" followed by "Original 22" and "Original 22 [Retro]", after which you will unlock Now And Then and be done with Rush Mode in regards to obtaining the Platinum. It isn't particularly hard as none of the Skull-Rated levels appear in these Rush Packs.