Black Mesa

Console cheese for these two achievements:

To spawn in the hat, use prop_physics_create props_junk/tomabasarab_quaff.mdl
then you need to appropriately name the hat; do this by pointing at it and using ent_setname quaff (the console should say "Set the name of prop_physics to quaff" after executing). Once this is done, bringing the hat through the appropriate portals will unlock the achievement.

For "Rare Specimen," you'll need to bring it through the portal to Xen at the very end of "Chapter 14 - Lambda Core." You can use map bm_c3a2i to get here quickly. You'll need to sit through the portal opening sequence, then throw the hat into the portal to Xen. The achievement will unlock as soon as you do this. You can use sv_cheats 1; god; sv_cheats 0 to toggle godmode and sv_cheats 1; noclip; sv_cheats 0to make this easier.

For "Rarest Specimen," you'll need to bring it through the portal to Nihilanth at the end of "Chapter 17 - Interloper," complete the Nihilanth fight, and wait for the G-Man to appear in the beginning of "Chapter 19 - Endgame" (when the achievement pops). G-Man should be wearing the purple hat when he appears; if he isn't, you did something incorrectly. You can use map bm_c4a3d1 and the aforementioned godmode and noclip commands to make this easier.

Console cheese for this achievement:

To spawn in the pizza box, use prop_physics_create props_canteen\pizza_box.mdl
then you need to appropriately name the hat; do this by pointing at it and using ent_setname drhornspizza (the console should say "Set the name of prop_physics to drhornspizza" after executing).

You'll need to bring the pizza box through the portal to Nihilanth at the end of "Chapter 17 - Interloper," complete the Nihilanth fight, and wait for the G-Man to appear in the beginning of "Chapter 19 - Endgame" (when the achievement pops). It should be raining pizza boxes when the G-Man appears; if it isn't, you did something incorrectly. You can use map bm_c4a3d1 and the aforementioned godmode and noclip commands to make this easier.

Just follow this simple walkthrough :

https://www.youtube.com/watch?v=R1gZEghZ5mw

You can follow this walkthrough to know where to find the hat and the pizza.
This video shows where the pizza/hat can be put idle during some game session.

https://www.youtube.com/watch?v=wWLIeJkVAlo

For this achievement you'll need to kill all 64 of the Protozoans on the chapters Xen, Gonarch's Lair, and Interloper. These are going to be the purple blobs that float throughout these levels and are generally pretty easy to find. There is one however that is in a hidden passage at the end of Gonarch's Lair. You'll have to bring the Cyanogen canister with you far enough to teleport it over there and then you'll have the passage opened. I go over all of the locations of the Protozoan's in my guide video.

For anyone having issues with the achievement (I had a LOT), here's what exactly what I did. My method is effortless and involves usage of console.

First, MAKE SURE that when you use noclip, you use the command sv_cheats 1; noclip; sv_cheats 0 or else achievements will be disabled. sv_cheats must be enabled and disabled in the same command to bypass all achievement unlocks being disabled for the rest of the game session.

You can noclip to the end of the map bm_c4a3c2, all the way up the level by the final set of a bunch of jump pads that send you to the next level transition. Then (and this is KEY), put in your console: achievement_reset BMS_LASER_IMMUNIZATION right before jumping off of the conveyor belt and onto the jump pads. People kept saying in Steam and Reddit threads to use this command before starting your attempts, and that's a good tip if you want to do the achievement without cheats, but if you are still having trouble and just want to unlock the achievement by any legal means possible, use the command at the END of your run, not at the beginning.

Some other details about my run specifically: I started Interloper from the main menu (didn't skip to map bm_c4a3b1 like some people suggested) and noclipped to the level transition point of each level leading up to map bm_c4a3c2. I went out of bounds in every level while noclipping. I also did NOT use godmode or buddha, but I highly doubt this would affect the achievement unlocking. I did not solve any puzzles nor did I even render/activate any of the lasers throughout the chapter. The key thing is: just use achievement_reset BMS_LASER_IMMUNIZATION right before the going off of the conveyor belt and onto the final jump pad.

For this achievement you'll need to bring all 6 of the possible followers during the chapter Office Complex over to the elevator shaft. You'll find them one by one throughout the chapter and have to bring them all to this elevator shaft alive. It's very useful to tell them to wait behind, clear up ahead, and then bring them through. This will ensure enemies don't kill them and they don't kill each other. I also made a video guide going over all of this.

Had a lot of trouble with this one. No matter what I tried, the guard kept getting spotted. When I noclipped to the door, (still inside of the hangar, next to the two crates) it finally worked out where I didn't get spotted, nor did the guard.

First off, this achievement is obtainable about midway through map bm_c2a5h. If you noclip to the point of this achievement, find the hangar, then backtrack (with noclip) to a room with big rusty pipes and white double doors. You need to open these doors to trigger the scripted sequence in the hangar section of the level.

Once the guard opens the door, noclip back outside of the map and back in right next to the red exit door. Just wait for the guard to stealthily make his way over to you. If you don't get spotted, he can't.