Arreya

Just wanted to say, 3 or 4 years later, this still works! Didn't need to start any particular quests to do this. Just sailed to the location, walked right in, killed the baddies to get to Mother Sharptooth and initiated conversation and ignored her a few times. Starting from 0 rep with Eder, just had to ignore Mother Sharptooth like 6-8 times (2 mins), then I got the "Burning Bridges" achievement (i.e. maximizing negative relationship with a companion).