I activate battlefield leadership and fires Leias gun. After her attack resolves, my opponent wants to play counter attack. Question is, does the other attack from Battlefield leadership trigger before counter attack?

Counter Attack says after an attack against you resolves. (It does not state it is an interrupt but in this instance I do not think that affects the timing sequence).

Although the bonus attack from the friendly figure provided by Battlefield leadership is stated as an interrupt there is a clear gap between perform an attack (so the attack is resolved) and then choosing another model. So after completion of the attack before resolving the then part of Battlefield leadership gives a window where Leia's attack has been resolved. So the counter attack occurs before the second attack. If Leia dies from the counter attack then she will be no longer be within 3 spaces of another friendly model to resolve the second part of Battlefield leadership. The interrupt occurs too late.

My apologies if this response turns out to be wrong but this seems the logical way the timings of the wordings occur.

When Leia performs the attack gained from Battlefield Leadership, and that attack resolves, Counter Attack can be used. After resolving Counter Attack (and potentially other abilities triggering from that) Battlefield Leadership can continue.