累坏 is a 'verb + result complement' —
累 ('tired') +
坏 ('to the point of breaking'). It almost always pairs with
了 (le):
累坏了, meaning the exhaustion has actually happened. Same pattern as
气坏了 (qìhuài le 'furious'),
笑坏了 (xiàohuài le 'laughed to pieces').