What makes these characters so special is that when they are obtained they join with some of the hardest hitting moves in the game I.E. Lini's Charge Ultima

Lini: Moogle Mog guard, Ultima Charge
Finish ANY mission successfully (be it Dispatch, Clan Turf, or Battle) with the mission item THE HERO GAOL set as one of the mission items you would like to bring along.

Eldena: Viera Barrier, Double Cast
Finish ANY mission successfully (be it Dispatch, Clan Turf, or Battle) with the mission item ELDA'S CUP set as one of the mission items you would like to bring along

Cheney: Human Capture, Ultima Shot
Finish ANY mission successfully (be it Dispatch, Clan Turf, or Battle) with the mission item SNAKE SHIELD set as one of the mission items you would like to bring along.

Pallanza: Bangaa Blitz, Ultima Sword
Finish ANY mission successfully (be it Dispatch, Clan Turf, or Battle) with the mission item WYRMSTONE set as one of the mission items you would like to bring along.

Quin: Nu Mou Giga Flare, Ultima Blow
Complete mission 063 - MISSING PROFESSOR. (This mission is located at the Tubola Caves)

Littlevilli: Viera Double Shot, Doom Archer
Complete mission 043 - CLAN LEAGUE. (This mission is located at Bervenia Palace) Littlevilli may offer to join your clan upon conclusion of the mission. To make mission 043 - Clan League available, you must complete Missions 40 through 42 (which become available after surviving against Llednar), read the rumour "Clan League Final", and complete the clan missions Yellow Powerz, Blue Geniuses, Brown Rabbits and White Kupos. (These are Reserve missions)