I have just been watching the highly accurate Troy (2004) directed by Wolfgang Peterson and all the warriors appear to wear breast plates and arm/shin guards. Is it accurate to depict ancient Greeks as wearing this type of armour and if so why were these particular areas deemed worthy of protection? Notably in the film several soldiers are hit in the thigh which appears to be lightly protected, why did they not think these areas needed protection?
You have already received an excellent answer but I really recommend reading this answer by u/Iphikrates.
There is also this cool podcast you can listen to about the movie.
I can't speak for how common arm and shin guards were in the era the Iliad is set in, as it is not my speciality. Troy (2004), as enjoyable a sword-and-sandal-flick as it may be considered, is of course far from an accurate depiction of the Iliad so I wouldn't use it as a guide on how well-armoured (or not) ancient Greeks were. However, I can speak to the general principles of what parts of the body would be armoured, and then apply it to the sort of warrior Troy seems to be going for.
When it comes to armour, there is a certain hierarchy that is replicated almost without fail throughout history and across cultures.
The first level of that hierarchy is the head or cranium, but not the face. If you could afford nothing else, you would still try to protect your head. Any attack to the head, with just about any weapon, could be fatal or at the very least incapacitating. In films you often see the hero fighting without a helmet, but this is complete nonsense - even the lowliest, poorest member of an army would at almost every point in history (notable exception is the period after the musket became so prevalent and effective traditional armour became obsolete, but before artillery became so effective that one would wear a helmet anyway to protect from shrapnel) would protect their head in some way. Even if just with a cap of padded cloth! I suspect this issue arises because directors want their star actors to be easily identifiable (and maybe the actors want their pretty mugs on display too). I think this is nonsense, as you can simply give them clearly distinguishable fancy helmets, but anyway...
The second level is the torso. Like with the head, an attack against the torso can be very dangerous. You have a lot of important organs there, and an attack against the heart or lungs especially could kill or incapacitate instantly. Puncturing organs like the spleen or liver will see you bleed out very quickly, while damage to the intestines would almost always mean a septic wound and thus death in pre-modern times. So you want to protect the torso! Again, even poor soldiers would look for protection, including simple padded cloth. It can be noted, in fact, that just padded cloth armour such as a gambeson is actually fairly effective at stopping (or at least minimising the damage from) a sword cut. Along with a helmet, some sort of torso-protection is the first armour to be added and the last to go - as gunpowder weapons increasingly made armour obsolete, and armour for the extremities were abandoned (despite a musketball being able to to terrible damage just by hitting a limb), cuirasses were still commonly used by pikemen and heavy cavalry. Note also that in modern warfare, protection for the torso, in the shape of kevlar vests and ceramic plating, has made a return.
The third level is the shoulders and tighs. The shoulders are a common target (strikes from above usually hit the head or shoulders) and it was thus not uncommon with extra armour there. Note for example how both the lorica hamata (the more common mail armour of Roman soldiers) and lorica segmentata (the more famous segmented armour of Roman soldiers) have additional cover for the shoulders. The tighs were also a prioritised target because of the femural artery. If that artery is cut, you will bleed out in literal minutes. The difficulty, however, is that when we start moving onto the extremitites, mobility becomes an issue. Thus, we see for example widespeard use of pteruges ("feathers" - layers of strips hanging from the cuirass, usually of rawhide, hardened leather or cloth) in the Greco-Roman world. In early medieval Europe, tighs were protected by making mail hauberks that extended down the tighs, and eventually also protecting the legs with mail chausses.
You'll note that we're yet to adress the shins and arms, which were the parts of the body you asked about. That's because everything I've mentioned earlier has a higher priority. You wouldn't bother protecting the arms and shins before the head, torso, tighs and shoulders were protected. Wounds to the arms and shins are rarely fatal, and they are also somewhat difficult targets to hit. However, we do see protection for the shins and arms. In fact, the Ancient Greeks did commonly wear shin armour, or greaves. When fighting as hoplites, their large apsis shields would cover most of the body, but not the shin. Thus, for a period it was common to wear greaves (or at least a greave on the leading leg) so that one would present a fully protected front. Generally speaking protection for the arms and shin was reserved for the rich or important - those who could afford full suits of armour or were sponsored by people who could.
Finally, there's the hands. Hand protection was actually quite rare. In part because its difficult to make effective protection for the hands without significantly hampering combat effectiveness, in part because a broken or cut hand won't kill you. And of course, one of your hands would likely be holding a shield anyway. That's not to say hand protection was unheard of - a knight or samurai in a full suit of armour would also have protection for the hands, and its not uncommon for weapons to include some sort of hand-guard.
So that's the entire body, except for two important exceptions: The face and neck. The face and neck are incredibly important to protect. In terms of the damage an attack could do, the face and neck are right up there with the head. The problem is that while a helmet can readily protect the cranium with weight and discomfort as the only drawbacks, protection for the face can entail blocking the senses and making breathing difficult. Protecting the neck can severely limit mobility. Because of this, the face and neck are special cases, where you see quite different practises across cultures and periods. You have examples like the Corinthian helmet hoplites are often depicted with - a helmet for a warrior that only needs to know what is right in front of him. Then you see the helmets typically used by Macedonians and Romans, and they are much more open in the face and around the ears, to make it easier to communicate and orient themselves on the battlefield.
The neck is as mentioned difficult to armour, though Medieval Europeans "solved" the problem with the mail coif, which offered a good balance between protection and mobility. Other solutions were simple scarves (which could actually be quite effective, especially when made of silk), aventails of various shapes, high collars.
So to summarise, pretty much everyone on the battlefield would have some protection for the head. It would also be very common with protection for the torso, even if just padded cloth. Next on the list would be the shoulders and tighs. The arms and shins were generally not a priority, and protection for the hands would be even more rare. The neck and face were special cases, with a lot of variation.
How would this apply to ancient armies? It depends on when. "ancient armies" is a very broad idea, and I'm not sure that the film Troy firmly establishes itself as any particular era. The warriors of the film look generally to be inspired by hoplites, in which case shin armour being common makes sense. While some might have worn vambraces, arm armour would generally be rare - when fighting with spear and aspis, the benefit of armouring one's arms is marginal compared to other parts of the body. Tighs would typically be protected with pteruges.