What is the biggest challenge in migrating existing infrastructure to a Cloud Platform?

That costs are doubling if you do not modernize your ecosystem - so in summary a "lift and shift" is costly. Public cloud makes commercially sense if you are dynamic on the usage and not running workloads 24x7 with high throughput. Second challenge is simply: trust and third one is the agility - you can see that as an advantage but have to adopt your lifecycles and processes also

Based on my experience:
1) Lack of a valid cloud strategy. Without answering the WHY Cloud with a clearly defined business outcomes, the cloud adoption is unlikely to yield any business value. 
2)  Determining the right migration strategy for workloads (using 7R framework). Lack of proper assessment will likely lead to overspend, performance issue, security compromise, non-compliance, etc.
3) Cost Management. Many think the cloud is cheaper .. it is not! Cheaper should not be your top reason for migrating to cloud. Migrating without measures in place to monitor and enforce cloud spend controls will likely lead to a heart attack moment when you get your first bill. 

There are other gotchas but  the above are the common ones I see often.

Policies and compliance. Then, the readiness of legacy systems including data. 

Some applications are not designed to be cloud-friendly, which can make it difficult to migrate them to the cloud. In some cases, it may be necessary to re-architect the application to take advantage of cloud-specific features and capabilities.

Corresponding administration know-how for managing the Cloud platform securely and performant.