First, ensure you have a stable environment to work with. This includes having access to a machine with Python installed, as we’ll use Python scripts to pull data from CoinMarketCap. Also, ensure TiDB is installed and running on your server. Verify connectivity between your Python environment and the TiDB server.

To access CoinMarketCap data, you need an API key. Sign up at the CoinMarketCap website and navigate to the API section. Register for an API key, which will be used to authenticate your requests to their server.

Use Python to fetch data from CoinMarketCap. You can use the `requests` library to make HTTP requests to their API. For example:
```python
import requests

api_url = 'https://pro-api.coinmarketcap.com/v1/cryptocurrency/listings/latest'
headers = {
'Accepts': 'application/json',
'X-CMC_PRO_API_KEY': 'your_api_key_here',
}

response = requests.get(api_url, headers=headers)
data = response.json()
```
This script fetches the latest cryptocurrency listings. Parse the JSON data to extract the information you need.

Once you have the raw data, process it to fit the schema of your TiDB database. This might involve selecting specific fields, transforming data formats, or cleaning the data. Create a function to transform this data into a list of tuples or a similar structure that matches your TiDB table schema.

Use a MySQL client library in Python, such as `mysql-connector-python`, to connect to TiDB. First, install the library if you haven’t:
```bash
pip install mysql-connector-python
```
Then, establish a connection:
```python
import mysql.connector

conn = mysql.connector.connect(
host='your_tidb_host',
user='your_tidb_user',
password='your_tidb_password',
database='your_database'
)
cursor = conn.cursor()
```

With the processed data and an active connection, write SQL queries to insert the data into your TiDB tables. Use SQL `INSERT` statements, and consider using `executemany()` for batch inserts to improve performance:
```python
insert_query = """
INSERT INTO your_table (column1, column2, column3)
VALUES (%s, %s, %s)
"""
cursor.executemany(insert_query, processed_data)
conn.commit()
```

After the data insertion, verify that the data is correctly inserted and consistent. Run `SELECT` queries on your TiDB database to ensure the data reflects the fetched CoinMarketCap data. Also, check for any anomalies or mismatches and address them by reprocessing or cleaning the data as necessary.

By following these steps, you can move data from CoinMarketCap to TiDB using direct API calls and manual data handling in Python, without relying on third-party connectors or integrations.