This is not exact, as for some characters multiple approaches will work or won't work at different times but if you follow these rules you will successfully complete the game. I will describe the characters rather than use their names to allow for maximum readability.

Sister and Little Brother: Spanish
Construction Worker: English (OR spanish every time for the professor achievement, this will damage your stars however)
Classmate/Friend: AAVE
Trio of Kids: English
LGBT Couple: English
Hipster: Spanish, English after he apologizes
Karen/White Lady: English will result in the lowest star loss but there are no options that will please her
Javi: Any approach is acceptable to Javi

A Productive Summer: Complete the game without getting fired

Ready to Work: Finish the tutorial

Thin Ice: Get to 3 stars, can be done as part of your "You're fired" run. The easiest way is to use exclusively either spanish or AAVE on everyone until you lose, doing this will also get you the Hablador Suave and Keepin It Real achievements.

You're Fired: Same as 3 stars, simply do the opposite of whatever communication style the customer wants

El Profesor: Speak to the construction worker in spanish every time you see him and this achievement will be awarced

Hablador Suave: Use only spanish until you get it
(10 times)

Keepin' It Real: Use only AAVE until you get it (10 times)

Employee of the Year: Follow the general guide to ensure you will not lose any stars

Best Fur-ends: click the cat ten times in a row

Time Machine: Respond "100%" when Javi offers you usage of his 'time machine'