All of these achievements are very self-explanatory and can either be obtained as side objectives while going through the story or in Endless Mode.
For the serving achievements you can use Endless Mode to grind them out while getting the achievements exclusive to Endless Mode. However should you not get them by the one hour mark, grind them out by repeating Day 1 of Story Mode instead as you get orders for each much more consistently there.

Double Cheeseburger, Medium Fries
Serve a customer a double cheeseburger, medium fries!


Oops, All Sauce
Use a whole sauce bottle when making a sundae.


Double Flip
Flip two patties at the same time in one clean motion.
Tip: While I’m not quite sure how this one is measured as it seems to not always work, you are limited to one shink sound when flipping the patties for it.

Burger Server
Serve 100 Burgers


Fry Server
Serve 2000 Fries.


Endless Servitude
Reach 10 minutes in endless mode.


Endless Servitude 2
Reach 1 hour in endless mode.

This section includes minor spoilers!

Perfect Breakfast
Eat every last bite of your breakfast.
At the start of Day 2 after getting up you'll make breakfast and eat it. Make sure to clear the plate in as little clicks as possible. As a tip place the food items on top of each other.

Trancend Reality
"Enjoy" the swings for an extended period of time.
In the park after using the swing once, use the swing again until you get the achievement.

Duck Feeder
Feed the ducks 100+ pieces of bread. (This is greatly unhealthy to them)
In the park head all the way to the right and feed the ducks. After feeding them once click on them again and continue feeding them until you get the achievement.

You too!
Say "you too" at a bad moment.
When getting your order say You too!

Just Here to Relax
Immediately sit on the bench at the park without doing anything else.
Self-explanatory.

Thanks, Dad
Make up with your dad.


(Argue)
(Refuse)
so sorry!
Go through the day until you are back home in the evening.
(Invite Dad to go to the park)

Nightcore Fan
Enable Nightcore mode at any time.
You can enable this in the settings while playing as Lilith.
You unlock Nightcore Mode by getting the Sleep Ending.

Poem Connoisseur
Rate one of Lilith's poems as Penelope.
Simply play Poetry Mode.
You unlock Poetry Mode by getting the Friend Ending.

This section includes spoilers!
After you completed Day 1 you always have the ability to do Day 2 and choose if Day 1 went good or bad when selecting the story, so you can grind out all the Day 1 Endings right away or later however you want without having to worry.

Day 1:

Bad Ending
Get the bad ending in day 1.
Waste a bunch of food like letting patties fall to the ground and generally do sloppy work.

Neutral Ending
Get the neutral ending in day 1.
Find a balance between working sloppily and working diligently. Letting around five patties fall and doing the rest somewhat well should work decently.

Good EndingGet the good ending in day 1.
Don't let any food fall. Stack the burgers correctly, the order goes left bottom up and then right top down, make sure to line them up well too. Generally just work diligently.

Day 2:

Sleep Ending
Get the sleep ending.
(Try to stay in bed)
(Commit to sleeping in)
Unlocks Nightcore Mode for Lilith.

Coworker Ending
Get the coworker ending.
Select Day 2 with Penelope having done bad on Day 1.
Unlocks Lilith in Endless Mode.

Friend Ending
Get the friend ending.
Select Day 2 with Penelope having done good on Day 1.
While talking to Penelope in the park: (Ask about yesterday) or (Say nothing)
Unlocks Poetry Mode.

True Ending
Get the true ending.
Select Day 2 with Penelope having done good on Day 1.

(Get up)
(Don't)
(Agree)
Do every activity in the park.
(Compliment her)
(Went on the swings)
(Cleaned up trash)
(Got a kite down)
(Fed the ducks)
(That's all)
Tell Penelope to quit her job
Unlocks the Epilogue.