Step 1: Understand the word.
A sycophant is a person who acts overly obedient or complimentary towards someone in power to gain advantage - commonly called a flatterer or yes-man.
Step 2: Find the synonym.
The key behaviour of a sycophant is excessive flattery and praise.
Step 3: Confirm.
Arrogant, superior, and critic all describe very different personalities. Flatterer directly captures the defining behaviour of a sycophant.
\[ \boxed{\text{flatterer}} \]