。
She tried to make him happy, but it was no use.
Literal
She [topic-は] him [object-を] tried-to-please [but-が] futile was.
喜ばせる is the causative of 喜ぶ ('be pleased') = 'to make happy / please.' The volitional + とする pattern ~ようとする means 'to try to / be on the verge of doing' — here 喜ばせよう (volitional of the causative) + とした (past) compresses 'tried to make (him) pleased.' The clause-final が is the soft contrastive 'but,' and 無駄だった ('was useless / in vain') delivers the verdict on the attempt. The full chain: 喜ぶ → 喜ばせる (causative) → 喜ばせよう (volitional) → 喜ばせようとする (try to) → 喜ばせようとした (past).