Spectral Force 3

To recruit Orochimaru (and Hototogisu), you need to complete the mission "Hiryu of the Far East".

Mission requirements: Recruit Rengeki, and then have the "Man of Mystery" conversation with him. This will trigger the mission, but it will not appear until you save your game.
Recruitment requirements: Neither Orochimaru or Hototogisu retreats; speak to Orochimaru with Rengeki, Eunice and Chulcha.

Once you have unlocked the mission, simply complete it without Orochimaru or Hototogisu retreating. Both will be present from the beginning and will actually help you out quite a bit. Be sure to keep an eye on Hototogisu, however, as she has a tendency to run off into large groups of enemies by herself. Heal both as needed and you should not have too many problems.Also be sure to have all three required party members move near Orochimaru and speak with him.

Both achievements will unlock after you have saved your game.

Thanks to LV 1 Blue Slime for the following strategy tip:
An effective strategy is to use two of your own characters to block in Orochimaru and Hototogisu so they can't run around and suicide. I didn't use Rengoku or Eunice, so I used them to block O&H in, and then used the other four to kill enemies. A big group will spawn near O&H but they will use their skills and possibly wipe half of them out before the enemies get up the hill. Clean up after that.