、。
As if to paper it over, I force a smile.
Literal
Paper-over-[as-if-to-ように], smile-[show-てみせる].
A terse narrative sentence from fiction. 取り繕う ('to paper over, to patch up, to make excuses') is specifically about covering up a mistake, awkwardness, or gaffe with surface appearances. ~ように ('as if to, in order to') with an activity verb marks purpose or manner. 笑ってみせる ('to smile, demonstratively') uses ~てみせる, which indicates doing something to show it off, for effect, or to prove something — distinct from ~てみる ('try doing'). So 笑ってみせる means 'put on a smile (for effect).'