I have completed that requirement for the aspiration and here's what I did:
1. Got both sims angry (from viewing angry painting). Sent them outside so no other emotional aura could interfere with the anger.
2. Had them do a couple mean interactions with each other.
3. Had the sim with the aspiration "Beg for Forgiveness." That alone didn't fulfill the requirement..
4. Had the sim "Apologize" (which showed up after I begged for forgiveness)
Here is the link to a thread that also mentions some difficulties with the soulmate aspiration, though it also includes separate aspiration discussion in the thread which can be a bit convoluting.