Alice proudly puffed out her chest with a triumphant 'Hmph!'
Literal
Hmph [quotative-と] greatly-boasting [with-で] Alice [topic-は] chest [obj-を] puffed-out.
えっへん is an onomatopoeia for a self-satisfied 'hmph!' or 'ahem!' — the sound of puffing up with pride. 大いばり 'great boasting / being very full of oneself' is a compound (大 'great' + いばり from 威張る 'to swagger'). 胸を張る 'to puff out one's chest' is the literal and idiomatic expression for showing pride.