Another thing that must be avoided is overusing compliments.
Literal
Avoid [must-なければならない] another one thing [topic-は], excessively compliments [object-を] use [nominalizer-こと] [copula-である].
避けなければならない modifies もう一つのこと as a relative clause: 'another thing that must be avoided.' 過剰に賛辞を使う = 'to use compliments excessively.' である is the formal copula.