To recruit Rato, you need to complete the mission "Dragon Jewel".
Mission requirements: Attain High Mercenary rank and the Meimai Knights are destroyed.
Recruitment requirements: Complete the mission.
Once you have unlocked the mission, simply complete it by defeating all enemies, including Rato. Once the mission is complete, Rato will join your party.
The achievement will unlock after you have saved your game.
Note:
Thanks to LV 1 Blue Slime for noting that defeating Rato ends the mission immediately, which I omitted to note.