If someone does something sycophantishly, they are acting in a way that tries to please someone in power, usually by flattering them.
The word sycophantishly has a negative feeling. It means someone is being fake or insincere to get something they want.
Examples:
He sycophantishly complimented the boss to get a promotion.
She sycophantishly agreed with everything the teacher said.
The man sycophantishly praised the king in hopes of getting a reward.
The cat sycophantishly purred to get more food.
The robot sycophantishly obeyed every command.
The parrot sycophantishly repeated everything the pirate said.