Yes, you do have to complete the Epilogue in Celeste to get the achievement.
Some of the achievements (or "challenges") in the game can be unlocked during the normal story mode, while other more challenging ones require you to complete special levels in the game's "B-Side" and "C-Side" story modes. Even more challenging achievements also require you to obtain all the "Strawberries" in the game.
The Celeste achievement requires you to finish the epilogue level (which is unlocked when you finish the game). The epilogue takes you back to the mountain, where Madeline will complete her journey by visiting all of the lost places and making her way back to the summit.
To get the Celeste achievement, you'll need to finish the Epilogue and make it to the top of the mountain. This can be tricky, but with a bit of practice and dedication, it is possible to complete.
If you're stuck on a particular section of the epilogue, there are tutorial videos online and a large community of Celeste players that are always ready to provide support and advice. In addition, there's also a Celeste Achievement Guide (https://guides.gamepressure.com/celeste_ps4/guide.asp?ID=50395) that you can use to make sure you're completing all the necessary steps to get your achievement.
Good luck and we wish you the best in completing the Epilogue and getting the Celeste achievement!