Pobedila sam protivnika.

Because the speaker is female.

In Serbian past tense, the main verb agrees with the subject's gender and number. So:

• pobedila sam = I (female) defeated
• pobedio sam = I (male) defeated

This is one of the first things English speakers notice, since English past tense does not show the speaker's gender.

Sam is the 1st person singular auxiliary form of biti (to be) used to form the past tense.

So the past tense here is built like this:

• pobedila = past participle
• sam = auxiliary am

Together:

• pobedila sam = I defeated / I beat

This is the normal Serbian past tense pattern.

Because sam is a clitic, and clitics in Serbian usually go in the second position of the sentence or clause.

So Serbian often prefers:

• Pobedila sam protivnika.

If you add ja, then the clitic usually comes after that first element:

• Ja sam pobedila protivnika.

Both are correct, but the short auxiliary sam normally does not stand freely the way English am/have does.

Because Serbian usually omits subject pronouns when they are not needed.

The form sam already tells you the subject is I, so ja is unnecessary unless you want emphasis or contrast.

Compare:

• Pobedila sam protivnika. = neutral, natural
• Ja sam pobedila protivnika. = I defeated the opponent (emphatic)

This is very common in Serbian.

Because protivnika is the accusative singular form, and it is the direct object of pobedila sam.

The dictionary form is:

• protivnik = opponent

But after a transitive verb like pobediti (to defeat), you need the direct object in the accusative:

• pobediti protivnika = to defeat the opponent

For masculine animate nouns, the accusative singular usually looks like the genitive singular, which is why you get -a:

• nominative: protivnik
• accusative: protivnika

Because that is a normal Serbian pattern for masculine animate nouns.

For masculine nouns referring to people or living beings, the accusative singular often matches the genitive singular:

• vidim čoveka = I see the man
• poznajem profesora = I know the professor
• pobedila sam protivnika = I defeated the opponent

But with masculine inanimate nouns, accusative usually looks like nominative:

• vidim sto = I see the table

So protivnika is exactly what you should expect, since protivnik is animate.

It is the past tense used in standard modern Serbian, often called the perfect.

Structure:

• past participle + auxiliary biti

So:

• pobedila sam = I defeated / I beat / I have defeated

In normal English translation, this will usually just be I defeated or I beat.

Pobediti is perfective.

That means it refers to a completed action: one finished victory, one successful result.

So:

• Pobedila sam protivnika. = I defeated the opponent.
  The action is complete.

Its imperfective partner is usually pobeđivati, which is used for repeated, habitual, or process-like situations, for example:

• Često sam pobeđivala protivnike. = I often defeated opponents.

In your sentence, the perfective verb is used because the victory is presented as a completed event.

Not necessarily. Protivnik usually means opponent, rival, or adversary.

It is commonly used in contexts like:

• sports
• games
• debates
• competitions
• elections

If you mean a true enemy, Serbian more often uses neprijatelj.

So in this sentence, protivnika most naturally means the opponent.

Yes. Serbian word order is fairly flexible, though not random. Different orders can change the emphasis.

For example:

• Pobedila sam protivnika. = neutral
• Ja sam pobedila protivnika. = emphasizes I
• Protivnika sam pobedila. = emphasizes the opponent
• Protivnika sam ja pobedila. = stronger contrast, like It was I who defeated the opponent

The clitic sam still tends to stay in second position, which is the main thing to watch.

Not exactly in the most direct sense.

Pobediti nekoga means to defeat someone / beat someone.

So:

• Pobedila sam protivnika. = I defeated the opponent.

If you simply want to say I won, Serbian often uses:

• Pobedila sam. = I won.
• Pobedila sam na takmičenju. = I won at the competition.

So your sentence specifically focuses on who was defeated, not just on the fact of winning.