Mothers try to show off their children's good points.
Literal
Mother [topic-は] own [possessive-の] children [possessive-の] good points [object-を] show-off-[try-ようとする]
見せびらかす = to show off/flaunt — a vivid compound with a slightly pejorative nuance. ~ようとする = 'try to.' The generic は makes this about mothers in general.