I finished the game on hardcore mode. But I didn't get any achievement to finish the game.

Well, this is the solution:
After completing the three missions Under No Flag, Tirailleur, Nordlys, enter the Under No Flag mission and press the Resume option, after that, the final video will be played again for you. After the video is finished, achievements will be given to you. .

Note 1: You don't need to find the letters or do the challenges to get the achievements.

Tip 2: Some friends said that you don't need to complete all stages on Hardcore mode to get the Hardcore achievement, you just need to finish the last ACT of the game on that level of difficulty.