Yes, there were small successes that saw Australian and New Zealand forces capture Turkish positions, the most famous of these, at least for Australians is the Battle of Lone Pine. The attack on Lone Pine was intended to be a diversionary attack to divert Turkish forces away from the real attack being made by the New Zealanders on Chunuk Bair. Both the Battle of Lone Pine and the Battle of Chunuk Bair were part of what became known as the August Offensive.

The initial attack on Lone Pine was difficult but ultimately successful though instead of diverting Turkish reinforcements, it instead attracted them to the north where they could be used to resist the New Zealand efforts at Chunuk Bair. Numerous attempts were made by Turkish forces to dislodge the Australians but ultimately it was held. Ironically, the diversion attack was the only attack that actually ended up succeeding. The fighting at Lone Pine was absolutely brutal. The Turkish defenders had covered their trenches with pine logs and when they finally got inside, the Australians found it difficult to identify friend from foe. This restricted them from firing their rifles and as a result, the fighting turned into a bloody melee with rifle butts, shovels, machete like bladed implements and pieces of timber used as weapons. There is a scene in the film The Water Diviner that illustrates the brutality of the Lone Pine assault fairly well, it's also a pretty good movie.

I hope that answers your question. If you would like me to elaborate on anything or if you have follow up questions just let me know, cheers