I haven’t played through everything yet, but the two events I know for sure are killing the wyverns for the refugees to gain respect. And fighting Bradley again to loose respect.
With killing the wyverns for the refugees, they will pay you a little for each wyvern you kill. They can only pay you for the quest once a day, but then offering to fight the wyvern again the same day will grant you respect. You can repeat this to get money and respect every day. However, after you defeat the Warlord, the quest is no longer available as far as I know.