Start by logging into your Mailgun account and navigating to the API section. Obtain your API key and relevant domain information. These details are necessary to authenticate and access data via the Mailgun API.

Use Python or any programming language that supports HTTP requests to interact with the Mailgun API. Construct an HTTP GET request to fetch the data you need, such as log events or message details. Make sure to handle pagination if you are dealing with large datasets.

```python
import requests

api_key = 'your-api-key'
domain = 'your-domain.com'
response = requests.get(
f'https://api.mailgun.net/v3/{domain}/events',
auth=('api', api_key),
params={'event': 'stored'}
)
data = response.json()
```

Once you have retrieved the data, process and clean it as needed. This may involve parsing the JSON response, filtering unnecessary fields, and transforming the data format to match the schema you plan to use in DuckDB.

```python
processed_data = []
for item in data['items']:
processed_data.append({
'event': item['event'],
'timestamp': item['timestamp'],
'recipient': item['recipient'],
# Add other necessary fields
})
```

If you haven't already, install DuckDB on your system. You can do this using pip if you are using Python:

```shell
pip install duckdb
```

Use DuckDB to create a new database file and define a table schema that matches your processed data. This can be done programmatically using Python.

```python
import duckdb

conn = duckdb.connect('mailgun_data.duckdb')
conn.execute('''
CREATE TABLE IF NOT EXISTS mailgun_events (
event VARCHAR,
timestamp TIMESTAMP,
recipient VARCHAR
-- Add other necessary fields
)
''')
```

Convert your processed data into a format suitable for insertion into DuckDB, such as a list of tuples. Then, use DuckDB’s `INSERT INTO` functionality to load the data.

```python
for record in processed_data:
conn.execute('''
INSERT INTO mailgun_events (event, timestamp, recipient)
VALUES (?, ?, ?)
''', (record['event'], record['timestamp'], record['recipient']))
```

Run queries on your DuckDB database to ensure that the data has been transferred correctly. Verify the integrity and completeness of the data by comparing sample records with the original Mailgun data.

```python
results = conn.execute('SELECT * FROM mailgun_events LIMIT 5').fetchall()
for row in results:
print(row)
```

By following these steps, you can effectively move data from Mailgun to DuckDB without relying on third-party connectors or integrations.