Using Azure Blob storage client library v12 for .NET, replace myaccount with the name of your storage account, mycontainer with your container name and myblob with the blob name for which the tier is to be changed:
var sharedKeyCredential = new StorageSharedKeyCredential("myaccount", storageAccountKey);
var baseBlobContainerUrl = string.Format("{0}.blob.core.windows.net", "myaccount");
var blobServiceClient = new BlobServiceClient(new Uri($"https://{baseBlobContainerUrl}"), sharedKeyCredential);
var containerClient = blobServiceClient.GetBlobContainerClient("mycontainer");
BlobClient blobClient = containerClient.GetBlobClient("myblob");
// Set access tier to cool.
await blobClient.SetAccessTierAsync(AccessTier.Cool);
If you are working with Azure Gov, use this url insteadl "{0}.blob.core.usgovcloudapi.net"
Keep in mind, your storage account should support Cool Storage.