Let's analyze the given information step-by-step to determine the order of heights:

1. Ananya is taller than Akanksha: This establishes that Ananya > Akanksha.
2. Ananya is shorter than Anushka: This adds to our understanding: Anushka > Ananya > Akanksha.
3. Anushka is shorter than Arya: This further refines the order: Arya > Anushka > Ananya > Akanksha.
4. Anushka is taller than Ananya: This is redundant information as it's already established in point 2. It serves as a confirmation of the previous statements' consistency.

Based on the combined information, the order from tallest to shortest is Arya, Anushka, Ananya, and Akanksha. Therefore, Arya is the tallest among them.

The key to solving this problem is carefully parsing each sentence and building a consistent height order, paying close attention to the comparative terms ('taller than', 'shorter than'). Redundant information, while not strictly necessary, often serves as a check on the accuracy of our interpretation of the relationships.