As to the specific noblewoman described by Imad ad-din, there was no such noblewoman. No other source records the arrival of a militarily powerful noblewoman in 1189, or at any other point in the Third Crusade. Noblewomen did participate, but almost always in the company of male relatives or family. For the church to allow a woman to go on a crusade, the woman required the permission of their husband or closest male relative. The closest thing to this mysterious crusader noblewoman was the participation of Eleanor, duchess of Aquitaine, on the Second Crusade 40 years before, in which she brought her own knights and demanded to exercise her feudal right (as their duchess) to command them in battle.

How true is this claim that the Crusades had women warriors?

The sources that claim this were almost all Muslim sources, which does suggest that it might be a propaganda thing to mock knights. However, several Muslim sources make independent claims about the participation of women which suggests that there may be more to it than that. In her article 'Women on the Third Crusade', Helen Nicholson lays out the issue with women and crusades:

Our problem is that in both the European Christian and the Muslim culture, it was expected that good, virtuous women would not normally fight, for it was believed that in a civilised, godly society women should not have to fight. Conversely, women were regarded as being particularly susceptible to evil. Therefore, Christian writers would not record women fighting in the crusading army, because this would discredit the crusaders - who had to appear as god-fearing in all their actions. On the other hand, Muslims would gladly depict Christians as allowing their women to fight, as this would show that they were either barbarous or degenerate people who had been led astray.

In other words, our Christian sources tend to deliberately edit out women where they were present, and our Muslim sources tend to make a big deal out of women wherever they appear.

But we do know that there were at least a few women who fought in the siege in some way. The most prominent of these was an archer described by Baha ad-din, an eyewitness:

One very intelligent old man... was amongst those who forced their way into the enemy's trenches that day. 'Behind their rampart', he told me, 'was a women, wrapped in a green mellita, who kept on shooting arrows from a wooden bow with which she wounded several of our men. She was at last overpowered by numbers; we killed her, and brought the bow she had been using to the Sultan, who was greatly astonished.

This is corroborated by Imad ad-din:

'There was a woman on one of the points of the defence holding a bow of wood, firing well and drawing blood; she did not stop fighting until she was killed.'

We can be pretty confident that this woman was a real person and good with a bow. She was also probably not the only female combatant, as many knights and noblemen travelled with their wives and female relatives, and those women often pitched in to help. It was extremely rare to see them on the front line, but they helped maintain the camp, assisted by filling in enemy trenches (and digging their own), and brought equipment such as arrows to those that needed them. The idea that some of these women might have thrown on some mail and picked up a sword at some point is not fantastical, especially in an emergency, though only this female archer is mentioned by the sources.

The stories of women in knight's armour are harder to assess. Imad ad-din isn't the only one to mention them; Ibn Al-Athir also discusses how several women equipped as knights were captured during a skirmish, but he seems to have used Imad ad-din as a source for this story so let's ignore him. The Muslim sources claim that only a handful of captives over the entire crusade were female knights, which does roughly match what we know about women in combat. Although women usually could not participate in knighthood - as the status of 'knight' was generally seen as an exclusively male one - they could still learn the skills, buy the armour, and fight the battles. Noblewomen, and sometimes the daughters of nobles, could potentially fight like knights if they wanted to and had the financial resources to afford it. For example, Isabel de Clare, the wife of the famed knight William Marshall, took an interest in knightly activities and went on to win battles when her lands in Ireland were invaded in the 1200s whilst William was with King John. This sort of thing - where the wife took the reigns (quite literally in Isabel's case) when their husband was otherwise engaged - wasn't seen as particularly odd as long as the woman in question had their husband's permission. Another example of a woman learning military skills is Judith, a daughter of King Henry I of England, who had her own retinue of 30 knights and was apparently very good with a crossbow. The Christian sources wouldn't tell us about it in a million years, but is not out of the question that women whose crusader husbands were wounded, busy elsewhere, or killed, might don their armour and participate in their stead if the husband had given their approval - there was limited precedent for it back in Europe.

So although this mysterious noblewoman was almost certainly made up, there were probably a few female warriors on the crusade.