She was furious at his words.

Literal

She [topic-は] his [genitive-の] words [at-に] fiercely belly [object-を] raised.

ひどく ('terribly, severely, badly') is the adverbial form of ひどい ('terrible, awful'). Here it intensifies the anger: 'fiercely got angry.' Stacks naturally with the 腹を立てる idiom — 'fiercely raised her belly' = 'was furious.' The に on ことば marks the trigger.