CT, regarding Super Shadows...
They're geared for extra challenge on your first run; if you've got experience with the game (like I did when I played the English version), beating them is reasonable, but your first few DOs, you probably should skip them. The "Reinforced" pieces are the only ones like this. They're noted by being bigger and armored.
Generally speaking, pieces are like this:
Silver Helmets: Weaklings
Silver Helmets with Pointy Objects behind them: Not weaklings!!! ...but still fairly easy to beat.
Armored Thingies: Tough enemies, usually one per Destiny Odyssey, you'll note their level is MUCH higher than anything else; good idea to skip them if you aren't confident.
Armored Thingies with pointy objects behind them: Replays of Maps only; these are the PSYCHO FREAK Manikens who exist so replays aren't total "You crush everything" and also exist to making getting DP Reqs easier for that 100%
Gold Pieces: Gimmicky. They have about the same AI level as the Pointy Objects one, maybe the Reinforced ones, but their levels and stats aren't absurd; however, they typically run off some weird thing, like they'll have Soul of the Destroyer, which gives 1000% Initial Brave (IE they will probably kill you instantly), but have 1 HP (so you do the same to them), so its quite literally a "whoever gets the HP Attack in first!" These guys often cheat with Phoenix Downs and take 2 shots however, but yeah. The gimmicks vary, where as the other pieces are all straight forward fights.
Don't worry about DP or tough pieces on your first run; the initial Destiny Odyssey Runs are to get a feel for the character, as well as some quick levels, and figure out who you awnt for SHade Impulse (as well as equipment and such.) Replays are where you start ripping your hair out for DP <.<