Before you start with the update, make sure you take backup of your website (code base & DB) or preferably, carry out this process on a staging site or on your local Drupal 8 set up. For this, it is assumed that you have composer installed for your Drupal 8 environment.

Modify compser.json

The first step is to modify composer.json manually.

1. Unset / empty “replace”: {},

2. Remove "merge-plugin" entirely.

3. Append “App\”: “app/”, “”: ”src/” to “autoload”

Once you are done with modifying the composer.json, it is time to execute a few commands with composer on CLI.
Execute composer commands

composer remove webflo/drupal-core-strict --no-update  composer remove drupal/core --no-update  composer require 'composer/installers:^1.7' --no-update  rm composer.lock  rm -rf core  rm -rf vendor  composer require drupal/core-recommended:^8.8 --update-with-dependencies  

Now, sit back and relax while composer performs the update. Once the updates are downloaded, it is time to perform the db updates using drush updb. Congratulations! You have successfully updated your existing Drupal 8 website to 8.8 and you are now ready for Drupal 9!