First, you need to obtain your Pivotal Tracker API token. Log in to your Pivotal Tracker account, navigate to your profile page, and find the API token section. You will use this token to authenticate your API requests and extract data.

Determine the specific data you want to export from Pivotal Tracker. This could be project details, stories, tasks, etc. Familiarize yourself with the Pivotal Tracker API documentation to understand the available endpoints and the structure of the data you wish to extract.

Use a tool like `curl` or a programming language with HTTP request capabilities (such as Python's `requests` library) to send GET requests to the Pivotal Tracker API endpoints. For example, using Python, you could fetch stories with:
```python
import requests

headers = {'X-TrackerToken': 'YOUR_API_TOKEN'}
response = requests.get('https://www.pivotaltracker.com/services/v5/projects/YOUR_PROJECT_ID/stories', headers=headers)
data = response.json()
```

Once you have the raw JSON data from Pivotal Tracker, process it into a format suitable for MySQL. This involves parsing the JSON and structuring it into tables and columns that correspond to your MySQL database schema. Ensure that you handle any nested data and convert it into a flat structure if necessary.

Set up your MySQL database with the appropriate schema to accommodate the data from Pivotal Tracker. Create tables with columns that match the structure you defined in the previous step. You can use a MySQL client or command-line interface to execute SQL commands for creating tables.

Write a script or use a MySQL client to insert the transformed data into your database. With Python's `mysql-connector` library, you can execute SQL `INSERT` statements like so:
```python
import mysql.connector

connection = mysql.connector.connect(
host='localhost',
user='yourusername',
password='yourpassword',
database='yourdatabase'
)
cursor = connection.cursor()

for story in data:
sql = "INSERT INTO stories (id, name, description) VALUES (%s, %s, %s)"
values = (story['id'], story['name'], story['description'])
cursor.execute(sql, values)

connection.commit()
cursor.close()
connection.close()
```

After loading the data, verify its integrity by comparing a sample of the data in Pivotal Tracker with your MySQL database. Check for data completeness and accuracy. Running SELECT queries in MySQL and comparing the results with the original data can help ensure that the migration was successful.

By following these steps, you can manually migrate data from Pivotal Tracker to a MySQL database without relying on third-party tools.