Upon completing the game once, you will unlock Challenge Mode. I would suggest completing the game once on Hard and unlocking this, and then finishing up everything else, leaving this and:
Once that is done, you can go ahead and flag Challenge Mode without having to beat the final boss one more time. Go to Extras and the option will be shown. What this offers is that you can unlock the Omega Weapons (Lv.6-10) and the Bolt Multiplier. Regular enemies will be slightly harder, but if you've dealt with Hard mode already, you can easily take care of the enemies by changing it to Casual (if that even matters). Just blow right through the story once more, ignoring everything else, and by the time you defeat the final boss one more time (especially with the Lv.5 or Omega Ryno, it should be FAST), you will finish this game up and get the Platinum.