"The achievements for Episode One and Two have been added to Half-Life 2. When launching the game it will attempt to read data from installed standalone Episodes to re-grant those duplicated achievements."
- https://steamproxy.net/steamstore/news/app/220/view/6633333780228604001

More specifically, the new "complete" version of Half-Life 2 will read the achievement status in the gamestate.txt files of the original base game and the two episodes:
...\steam\steamapps\common\Half-Life 2\hl2\gamestate.txt
...\steam\steamapps\common\Half-Life 2\episodic\gamestate.txt
...\steam\steamapps\common\Half-Life 2\ep2\gamestate.txt
and "sync" them into one overall file:
...\steam\steamapps\common\Half-Life 2\hl2_complete\gamestate.txt

The gamestate.txt files will be present if some achievement progress has been made, and are created/updated when quitting the specific game or viewing the in-game achievement list.

Install and launch the two episodes separately - find them in the Steam Library with the filter set to "Tools" instead of "Games", or go to their Store page and select "Play Now" or "Play Game":
Half-Life 2: Episode One
Half-Life 2: Episode Two
It should not be necessary to view the in-game achievement lists, but it won't hurt.

Once the older gamestate.txt files are present, launch Half-Life 2, and the previously unlocked achievements for the episodes will pop all at once.

(Achievements earned in the "complete" version can NOT be transferred back to the individual standalone episodes.)

In Half-Life 2 - "Lambda Locator"
In Half-Life 2: Episode 2 - "Piñata Party" & "Cache Checker"

Progress on these three achievements is stored in the gamestate.txt file, which is not saved to the Steam Cloud, so ALL items must be collected on the same PC. The items can be collected in any order, across multiple playthroughs, and only need to be collected once.
The "fix" below will not work for these cumulative achievements, unless you want to collect all of the items again.

For help finding missed caches for Lambda Locator, see this guide: https://steamproxy.net/sharedfiles/filedetails/?id=2083709328
The "sync" of achievements done by the "complete" 20th Anniversary version may prevent further progress on cumulative achievements, due to the old gamestate files repeatedly being used to overwrite the new one.
So after the initial "sync" of achievements, rename (or delete) the old gamestate.txt files in the hl2 and ep2 folders.

Achievements show as unlocked or completed on the in-game menu, but not on Steam.

Possible causes:

• There is something unreliable about the way Half-Life 2 communicates with Steam.
  
• Temporary loss of connection with the internet or Steam server.
  
• Two players are using Half-Life 2 on the same computer (either they both own the game, or are using Family Sharing). Achievements may only unlock for the first player who completes them.

If an achievement does NOT show as unlocked on the in-game menu, then not all of the requirements for the achievement have been met.

Achievements will NOT unlock in these cases:

• Steam Client in Offline Mode, or loss of connection while playing.
  The in-game Achievements list will not be available; instead, this message will be displayed:
  "You must be logged in to Steam to unlock or view Achievements."
  (Quit the game, restart your PC and modem, and try again.)
  
  
• Cheats active (sv_cheats 1) at any time during your play session.
  
• Commentary mode (it activates cheats)

To ensure commentary mode and cheats are off, start a New Game at any chapter with commentary disabled.

Quit Half-Life 2, if it is running.

Delete this file:
...\steam\steamapps\common\Half-Life 2\hl2\gamestate.txt
and rename *(or delete) this file:
...\steam\steamapps\common\Half-Life 2\hl2_complete\gamestate.txt

Make sure you are online AND connected to Steam.

Then start Half-Life 2, and REPLAY the part relevant to the achievement.


(This will not affect any achievements already unlocked on Steam.)

* If you are part-way through any "cumulative achievements", "rename" the file to keep as a backup (for example: "gamestate.txt.bak" or "gamestate - backup.txt"), and read below.

To easily find where your game files are stored:
In your Steam Library, select Half-Life 2, select Manage (gear icon), then Manage > Browse local files

If you have the "Hide extensions for known file types" option enabled in your file browser, the file name should appear as "gamestate", with the "Text Document" type.

Half-Life 2 uses a local file named gamestate.txt (shared by all players using the same computer) to record progress with achievements - if they are already unlocked, they won't be triggered a second time.

The gamestate.txt file is not part of the original install of the game. It is only created AFTER you have made achievement progress.

When you start Half-Life 2, the game checks both the local gamestate.txt file and the online list of achievements associated with your Steam account, and combines them in to the list of achievements displayed in-game. Each time you quit Half-Life 2, the gamestate.txt file gets re-created based on the combined progress. After using the fix, you can delete the new file and replace it with the file you renamed earlier. (Actual progress on "cumulative achievements" will be lost if you don't keep the original file.)

In each case, you only need to replay the exact moment where the achievement is triggered. So use a saved game, if you have one (unless cheats were active). If that doesn't work, try starting a New Game from the nearest chapter.

Since the problem is about Half-Life 2 communicating with Steam, even the fix may not work the first time - so TRY AGAIN!

Verify Integrity of Game Files:
https://support.steampowered.com/kb_article.php?ref=2037-QEUH-3335

Clear Download Cache:
https://support.steampowered.com/kb_article.php?ref=3134-TIAL-4638

5 of the 33 achievements for the base game Half-Life 2 are "hidden".
Details for hidden achievements are fully revealed once they are unlocked.

The in-game achievement list completely ignores hidden achievements until unlocked, so it may show 100% completion while hidden achievements are still incomplete. For example, with 1 remaining hidden achievement it will show 32/32, even though there are actually 33 in total.

To see details for the hidden achievements, open the achievement list from your Steam Library, select Global Achievements, and "click to show spoiler" for any that are hidden.

https://steamproxy.net/sharedfiles/filedetails/?id=419856706