What it meant by "you can catch a Cactuar" is that if you complete Large Hard Cup once more, you'll unlock Cactuar Cup. Though the feat is usually semi-impossible since all of a sudden, terrors from the Via Infinito (Black Elemental + Mushroom Cloud, Mega-Tonberry) appear in the Large Hard Cup... though your final enemy is always Areq + Arroja.
Well I find certain cups have teams which regulary have a high chance of you having to battle them at some point in the cup (main event teams as I call them) For instance Regular Cup has Team Odd Couple which you'll mostly encounter at some point Large Cup you'll have either Darkness or Raging River which will cross your path often and get to the finals Large Hard Cup Main Events will normally be either Black Mist or The Reaper
To catch a cactuar you must be in chapter 5. To be more specific you need to unlock the Rogue Cactuar lair for them to appear at all
My UCG: http://www.scribd.com/doc/86352624/FFX-Ultimate-Companion-Guide-v1-0 My Youtube: http://www.youtube.com/user/ppbirdman