Nessuna azienda mi ha ancora assunto, ma una mi ha già chiamato per un secondo colloquio.

Both can express no company, but nessuna azienda is the most natural direct way to say it here.

• Nessuna azienda mi ha ancora assunto = No company has hired me yet
• You could also say Non mi ha ancora assunto alcuna azienda, but that sounds more formal or literary.

So for everyday Italian, nessuna + noun is very common and straightforward.

Because it talks about events connected to the present:

• mi ha ancora assunto = has hired me yet
• mi ha già chiamato = has already called me

In Italian, passato prossimo is often used where English uses the present perfect. It fits well because the speaker is talking about their job search up to now.

Here ancora means yet.

So:

• Nessuna azienda mi ha ancora assunto = No company has hired me yet

Depending on context, ancora can also mean still or again, but in negative sentences like this one it often corresponds to yet.

Già means already.

• una mi ha già chiamato = one has already called me

It contrasts nicely with ancora in the first clause:

• not hired me yet
• already called me

This creates a very natural contrast: nothing final has happened yet, but some progress has already happened.

Mi is the indirect/direct object pronoun meaning me, depending on the verb.

In this sentence:

• assumere qualcuno = to hire someone
  → mi ha assunto = hired me
• chiamare qualcuno = to call someone
  → mi ha chiamato = called me

Italian object pronouns usually come before the conjugated verb:

• mi ha assunto
• mi ha chiamato

Here una means one (company).

It replaces un’azienda to avoid repetition:

• Nessuna azienda... ma una...
• literally: No company..., but one...

This is very natural in Italian. The noun azienda is understood from the previous clause.

Because with avere in standard usage, the past participle usually does not agree with the direct object.

So you normally say:

• L’azienda mi ha assunto

not necessarily:

• L’azienda mi ha assunta

Even if the speaker is female, everyday Italian commonly keeps assunto unchanged after avere.
You may sometimes hear agreement in some contexts, but for learners, the safest rule is:

• with essere: agreement is required
• with avere: agreement is usually not made

Because chiamare per is a common pattern meaning to call someone for something.

• mi ha chiamato per un secondo colloquio = called me for a second interview

Here per expresses the purpose or occasion of the call.

A few similar examples:

• mi hanno chiamato per un test
• ti chiamo per una riunione
• l’hanno chiamata per un lavoro

In this context, colloquio means interview, especially a job interview.

• primo colloquio = first interview
• secondo colloquio = second interview

The full expression colloquio di lavoro means job interview, but Italian often shortens it to just colloquio when the context is clear.

The word order is natural and idiomatic, especially because of the adverbs and pronouns:

• Nessuna azienda mi ha ancora assunto
• una mi ha già chiamato

A few points:

• mi normally comes before ha
• ancora and già often come between the auxiliary and the past participle
• ma introduces the contrast: no one has hired me, but one company has called me back

You could change the order slightly for emphasis, but the original version is the most neutral and natural.

Because both verbs here take avere in the passato prossimo:

• assumere → ha assunto
• chiamare → ha chiamato

In Italian, some verbs use essere, but transitive verbs like these usually use avere.

Since both verbs take a direct object (me), avere is exactly what you expect here.

They are close, but not identical in tone.

• Nessuna azienda = neutral, standard, everyday no company
• non una sola azienda = more emphatic, like not even a single company

So the original sentence is the normal way to say it. If you wanted stronger frustration or emphasis, you might choose a different structure.