Nigo is a Friendly Enemy until Ichigo beats her in combat, at which point, battered, humiliated, and barely able to move, she declares her undying hatred for Ichigo.
Ichigo dodges Nigo's attacks, but refuses to fight back, and wins Nigo's friendship by refusing to hurt her.
Ichigo, in an odd Enemy Mine situation, has to help her sworn enemy, Nigo. Nigo later does a Heel-Face Turn after this, since, despite all the blood that's been shed, all the punches thrown, all the beatdowns they've given each other, she's gotta respect the fact that Ichigo, of all people, came to her aid.
Ichigo befriends Nigo, then defeats her.
Subverted: Ichigo defeats Nigo and asks for a handshake of friendship, but is refused.
Double Subverted: It's only after a heartwarming speech that Nigo accepts her friendship.
Ichigo pokes Nigo, causing Nigo to dedicate the rest of her life to her.
Zig Zagged: Ichigo defeats Nigo in combat and offers to be her friend but Nigo refuses. Then Ichigo makes a heroic speech and she accepts but it was a fake defection to inflitrate Ichigo's group. Over time Nigo reconsiders after experiencing the perksof being a hero. However her ruse is exposed and the hero team turns on Nigo and she fights back, doing great damage to the Home Base as if she truly were The Mole. She and Ichigo fight again, but this time Ichigo only disarms her and gives her a Cool Down Hug. The rest of The Team still doesn't trust her so the pair run off to form their own side.
Ichigo defeats Nigo and they remain at odds.
Ichigo befriends Nigo without beating her.
Enforced: "Nigo's turned out to be very popular with the fanbase, and the merchandise with her sells well. Rather than have her die at the end of the season, how about Ichigo defeats Nigo once and for all, and Nigo becomes her friend?"
Lampshaded: "By defeating me, you've earned my respect".
Invoked: Nigo knows Ichigo respects a fair victor and sets out to defeat her in order to gain her alliance.
Exploited: In Nigo's culture, a defeated fighter must pledge his life to a victor who spares his life. Ichigo knows this and deliberately provokes a reluctant Nigo into a Duel in order to recruit him.
Shin places Nigo, and his other minions under mind control to prevent this sort of thing from happening.
Ichigo refuses to accept Nigo's friendship until they've both had a chance to catch their breath and think things over, just to be sure the adrenaline isn't clouding Nigo's judgement.
"Am I hearing you right? You just beat the hell out of me, and now you want me to be your pal? Are you a sociopath, or just a moron? Either finish me off or leave me the hell alone, Ichigo!"
Nigo surrenders without a fight, out of fear that Ichigo will killer her if she resists.
Discussed: "Ichigo, have you noticed that all your friends are your ex-enemies?"
Conversed: "This new character, Nigo's kind of cute; I hope she and Ichigo will make up after Ichigo beats the crap out of her".
Nigo joins Ichigo out of fear that the next time they fight, it will be fatal, and is scared of Ichigo even in their normal lives, as if she was a bully.
Alternative: Ichigo doesn't let Nigo join her True Companions because of kindness, but of pragmatism. Ichigo is aware that letting her enemy join her team after a beat-down reather than outright kill her off is of strategic advantage in case of future conflicts, and with Nigo's powers, that's something she just can't say no to. The reason why Nigo accept Ichigo's offer to join her team is because it's either that or getting her head bashed in.
Another alternative: Ichigo's offer of friendship is genuine, but Nigo only joins because she fears what her superiors will do to her if she returns in defeat, not because of Ichigo's kindness.
Fifth alternative: In the process of trying to make Nigo listen to her through superior firepower/kung-fu/magic, Ichigo inadvertently kills her.
Over time, however, Nigo learns that Ichigo isn't really all that bad, and begins to genuinely appreciate and befriend her.
Alternative: Ichigo and Nigo live a culture where friendship IS pragmatism; both strong friends and loyal friends. A fight demonstrates the strength and mercy builds loyalty.
Another alternative: Nigo becomes Ichigo's Token Evil Teammate with Undying Loyalty to Ichigo, because Ichigo was kind enough to spare her (something her superior would never do) and then personally nursed her back to health.
Fifth Alternative: Ichigo's uses non-lethal weapons when attempting to "befriend" Nigo. If she inadverently goes too far the worst that can happen is knocking her unconscious. When she wakes up they can continue the conversation.