Learn Turkish: Patron seni aşırı övdü. - The boss praised you excessively.

The verb övmek means to praise someone else. Since the boss is praising you (seni), the action goes to another person. If the boss were praising himself (boasting), you would add the reflexive -(i)n suffix to make övünmek (to boast), and the sentence would be Patron aşırı övündü (The boss boasted excessively).

Why is it seni instead of just sen?

Sen (you) gets the specific direct object (accusative) ending -i because you are the one receiving the action of the praise. Whenever a specific person or pronoun is the direct object of a verb, it must take this ending.

Is aşırı an adjective or an adverb here?

It is acting as an adverb here because it describes the verb övdü (praised). Aşırı is very flexible in Turkish and can mean both 'excessive' (adjective) and 'excessively' or 'extremely' (adverb).

Could we say Patron aşırı seni övdü instead?

It sounds a bit unnatural. In Turkish, the word right before the verb gets the most focus. Putting aşırı right before övdü correctly emphasizes how the boss praised you. Moving seni between them breaks that focus.