I like splitting up the phrases of quotes like this to make it easier to understand.
"After some 6 weeks fatting amongst those savage courtiers" – after character has spent 6 weeks preparing for execution (lamb fattened for slaughter)...
"At the minute of my execution" – just before/as I was about to be executed...
"she hazarded the beating out of her own brains to save mine" – she (feminine character) risked her own life (beating out of brains = death) to save his life.