Learn Hardcore Japanese: watasi ha sono eiga wo nikai mimasita.

In Japanese, は marks the topic of the sentence—“as for me”—while が marks the subject in a neutral or identifying sense. Here, 私 is setting the topic (“I, as for me, …”). You could use が in contexts like 私が行きます (“I’m the one who will go”), but with actions you commonly want は. You can also omit 私は entirely if context makes it clear who’s speaking:
その映画を二回見ました。 still means “I watched that movie twice.”

What does その mean in その映画, and how is it different from この or あの?

その is a demonstrative adjective meaning that (near you/the listener). It refers to something both speaker and listener know.

この映画 = this movie (near the speaker)
その映画 = that movie (near the listener or already mentioned)
あの映画 = that movie over there (distant from both)
Use その映画 when you’ve just talked about the movie or it’s known to your listener.

Why is を used after 映画, and what does it indicate?

The particle を marks the direct object of a transitive verb. Since 見る (“to watch/see”) takes 映画 as what’s being watched, you need 映画を to show it’s the object:
その映画を見ました。

Why does 二回 come before the verb without a particle? Could I use に?

Counters like 二回 (twice) are adverbial nouns in Japanese, so they can modify verbs directly without particles:
二回見ました。 (“watched twice”)
You don’t say 二回に見ました. If you switch to an ordinal meaning (“for the second time”), you add 目 and then に:
二回目に見ました。

What’s the difference between 二回 and 二回目?

二回 = cardinal count “two times” or “twice,” used adverbially (no particle).
二回目 = ordinal “the second time,” so it needs に to modify the verb: 二回目に見ました (“I watched it for the second time”).

What tense and politeness level is 見ました? Could I say 見た instead?

見ました is the past tense polite form of 見る (“to see/watch”). It’s appropriate in most conversations with people you don’t know well or in polite contexts. 見た is the plain past form, used among friends, family, or in casual writing.

Can I change the word order, like putting 二回 at the very beginning?

Yes. Japanese word order is flexible thanks to particles. For example:

二回、私はその映画を見ました。 (Emphasizes “twice.”)
その映画を、私は二回見ました。
The key is keeping each element with its particle. The neutral order is Topic + Object + Frequency + Verb.

Are there other ways to say “twice” besides 二回, and do they differ in nuance?

Yes. 二度 (にど) also means “twice” and is slightly more formal or literary. In spoken Japanese, 二回 is most common. You might see ２回 in casual digital text. Both convey the same basic idea.