I'll be going through all of the unmissable story achievements first, and then get into the more nuanced achievements that you may need to be purposefully trying to get.
This guide is split into 2 parts. This is part 1.
Chapter - Point Insertion
On the chapter “Point Insertion'' when you’re in an apartment, and it gets raided by the combine, you’ll have to start running. Once you run across the roof for a block or two you’ll go into a window and the achievement will pop up.
Chapter - A Red Letter Day
After having to run out of Dr. Kleiner’s lab on the chapter “A Red Letter Day” Barney will drop you down your trusty crowbar. Pick it up, and the achievement will pop up.
Chapter - Route Kanal
A little bit later on the chapter “Route Kanal” you’ll run into a resistance fighter that has gotten an airboat ready for you. Once you get in it and take off you’ll get the achievement.
Chapter - Water Hazard
While going through this chapter you’ll come across a resistance camp. A vortigaunt will mod the airboat with a turret which will unlock this achievement.
Chapter - Water Hazard
Once you have the turret attached to your airboat on the chapter "Water Hazard," you'll then be able to defeat the hunter-chopper later on that level. Once it has been destroyed you'll get this achievement.
Chapter - Black Mesa East
For this achievement you’ll need to get the gravity gun in the chapter “Black Mesa East.” After arriving here Alyx will take you out into Eli’s junk yard and give you the gravity gun which will unlock the achievement.
Chapter - We Don't Go To Ravenholm
While on the chapter "We Don't Go To Ravenholm" Father Grigori will meet up with you and you’ll start going through a cemetery filled with zombies and headcrabs. Once you escort him safely through you’ll receive this achievement.
Chapter - Highway 17
While on the chapter "Highway 17" you'll come up to a small base called Little Odessa. For this achievement you'll need to defend this base from the gunship attack. Once it has been destroyed you'll receive the achievement.
Chapter - Entanglement
This achievement is for surviving the second turret standoff in Nova Prospekt. During the chapter “Entanglement” you’ll have to defend Alyx and the teleporter with a few turrets at your disposal. Once you get through the fight and teleport away you’ll get the achievement.
Chapter - Anticitizen One
For this achievement you’ll need to gain command of a squad of rebels during the uprising. The first time you’ll get a squad of rebels is at the beginning of the chapter “Anticitizen One.” A group will run up to you automatically unlocking the achievement.
Chapter - Anticitizen One
For this one you’ll need to get through the toxic tunnel in City 17. This will happen later on in the chapter “Anticitizen One” while leading a squad of rebels. You’ll come to a locked door which only you can unlock. You’ll go through that radioactive tunnel and then unlock the door from the other side, activating the achievement.
Chapter - Anticitizen One
For this one you’ll need to survive the generator plaza standoff in the chapter “Anticitizen One.” Later on in this chapter Alyx will join you again and start disabling a generator. During this time multiple waves of Combine soldiers will attack, and once Alyx finishes you’ll get the achievement.
Chapter - Follow Freeman
For this one you’ll need to shut down the suppression device on the chapter “Follow Freeman.” After meeting up with Barney you’ll get to the nexus building which you’ll then have to disable multiple energy ball reactors. Once that is done Barney will finish disabling the suppression device and the achievement will unlock.
Chapter - Follow Freeman
For this achievement you'll need to survive the rooftop strider battle in City 17. This will be later on in the chapter "Follow Freeman."
Chapter - Dark Energy
This one is for destroying the citadel’s reactor core and finishing the game. At the end of the chapter “Dark Energy" you’ll have to fight two gunships with energy balls and then shoot the energy balls into the large reactor until it is destroyed.
Chapter - Point Insertion
For this achievement you'll need to hit the trash can cop with the can. At the beginning of the game on chapter “Point Insertion” when the cop knocks over a soda can and tells you to pick it up you can grab it and throw it at him to unlock this achievement.
Chapter - Point Insertion
For this one you'll need to put the can in trash. At the beginning of the game on the chapter "Point Insertion" a cop will knock a can over and tell you to pick it up. If you do as he says the achievement will pop up.
Chapter - A Red Letter Day
For this one you’ll need to break the mini-teleporter in Kleiner’s lab on the chapter “A Red Letter Day.” If you just keep teleporting the cactus back and forth eventually it will break and the achievement will pop.
Chapter - Route KanalFor this one you’ll need to kill five barnacles with one barrel. You can do this on the chapter “Route Kanal” pretty easily. Once you get to this slime tunnel you’ll see a large amount of barnacles. Grab an exploding barrel and throw it down. Shoot it once it gets close to them to blow it up and you’ll get the achievement.
Chapter - Water Hazard
For this one you’ll need to find the hidden singing Vortigaunt in a cave on the chapter “Water Hazard.” Right after you destroy the hunter-chopper you’ll need to open the gate and go straight ahead to a couple of large drain pipes. You’ll need to park the airboat under the left one and climb up into the pipe. Jump run all the way through and to the left as it is radioactive in here and you’ll take damage going through there. You’ll come up to a camp with the Vortigaunt and activate the achievement.
Chapter - Black Mesa East
For this one you’ll need to pick up the HEV suit charger faceplate in Eli’s scrapyard. Once on the chapter “Black Mesa East” you’ll go into Eli’s scrapyard and receive the gravity gun. Up on the area above there you’ll need to climb up and grab the faceplate with the gravity gun.
Chapter - Black Mesa East
For this one you’ll need to use DOG’s ball to make a basket in Eli’s scrapyard. Once you play catch with DOG you can start trying to throw the ball into the basket ball hoop. It took me a few reloads to get this before the combine came so it may take a few tries.
Chapter - We Don't Go To Ravenholm
For this one you’ll need to play through the entire chapter of “We Don't Go To Ravenholm” while only using the Gravity Gun. If you accidentally switch to a gun or something as long as you do not fire it, throw anything, or switch your crowbar you’ll still be able to get the achievement. Taking a circular blade with you through the chapter will help a lot with this.
Chapter - Highway 17
For this one you’ll need to kill 3 enemies using the crane on chapter “Highway 17.” Once you use the crane and the three combine soldiers run out, just pick things up and drop it on top of them until they are all dead.