Challenge Mode is unique to the PSP version of LSWII. This mode allows you to enter the level as any character, and you are tasked with finding 10 Blue Canisters in about 10 Minutes. You'll get no studs, and you can't use any Extras, so it's a simple case of finding all 10 to unlock some characters from LSWI.
In general, it's a good idea to memorise how many characters until your primaries. You'll also want to note where the Protocol, Astromech, Bounty Hunter and Sith are, so you can switch to them quickly.
A common thought is to use a Ghost in these stages, as you can't be hit. Althought any character works fine.
You can actually tackle these as early as completing Story of IV-3, as you can get a Sith (Maul or Dooku) from the Prequel stages. A Bounty Hunter from IV-3 (Greedo), and an Imperial from IV-1 (Stormie). You can also get a Shortie (Jawa), from IV-2 if needed. Pretty much everyone you need to complete these stages (and by extension, Free Play Mode).