Begin by reviewing the Mailjet API documentation to understand the endpoints that will allow you to retrieve the necessary data. Identify what data you want to move (e.g., email campaign statistics, contact lists) and note the structure of this data.

Log into your Mailjet account and navigate to the API key section. Generate an API key and secret, which you will use to authenticate your requests to the Mailjet API. Ensure that you have the necessary permissions to access the data you intend to migrate.

If you haven't already, install Boto3, the AWS SDK for Python, which will allow you to interact with DynamoDB. You can install it using pip:
```bash
pip install boto3
```

Write a Python script to connect to the Mailjet API using the requests library. Use your API key and secret to authenticate, and make GET requests to the relevant Mailjet endpoints to fetch the data you need. Here's a basic example:
```python
import requests

api_key = 'your_mailjet_api_key'
api_secret = 'your_mailjet_api_secret'
endpoint = 'https://api.mailjet.com/v3/REST/contact'

response = requests.get(endpoint, auth=(api_key, api_secret))
data = response.json()
```

Once you have the data from Mailjet, process and format it to match the requirements of your DynamoDB table. Ensure that each item in the data set maps correctly to the attributes defined in your DynamoDB schema. This may involve data transformation or re-structuring.

With the AWS SDK (Boto3), connect to your DynamoDB table and insert the formatted data. Here's a basic example of how to put an item into a DynamoDB table:
```python
import boto3

# Initialize a session using Amazon DynamoDB
session = boto3.Session(
aws_access_key_id='your_aws_access_key_id',
aws_secret_access_key='your_aws_secret_access_key',
region_name='your_aws_region'
)

# Initialize DynamoDB resource
dynamodb = session.resource('dynamodb')
table = dynamodb.Table('your_dynamodb_table_name')

# Insert data into DynamoDB
for item in formatted_data:
table.put_item(Item=item)
```

After the data migration, verify that the data in DynamoDB is complete and consistent with the data in Mailjet. Perform checks to ensure that all expected records are present and that the data integrity is maintained. You might want to query the DynamoDB table and compare it against the original dataset.

By following these steps, you can effectively move data from Mailjet to DynamoDB without using third-party connectors or integrations.