I'm a dual status alien (resident alien for 4 months and non resident alien at end of 2018 ). Can I use Child Tax Credit for the part of year that I was a resident alien?

Yes, if your dependent qualifies for the child tax credit.  To file a dual status return you MUST use itemized deductions.  You are not allowed to use the standard deduction.  Below are the instructions for suppressing the standard deduction in TurboTax.  Also, you can only use the filing status of single or married filing separately.

You will need to file a dual status tax return for 2018 as you were a part year resident and part year nonresident.

In order to prepare a dual status return in TurboTax, you will need to print a copy of the nonresident return (Form 1040NR from the IRS website) for your tax on US income after May. There will most likely be no US source income to enter for that time.  So your income on this form will probably be zero unless you received US income after moving out of the US.. Write on the top of the 1st page of the 1040NR, Dual Return. You will need to write in your name and address and input zero as your US source income (if that is the case).

https://www.irs.gov/pub/irs-pdf/f1040nr.pdf

Then for the resident part of the return you prepare in TurboTax, you are not allowed to use the standard deduction, only itemized deductions if you are filing a dual status return.  Also, you can either file single (if you are single) or married filing separately.

You must suppress the standard deduction.  Instructions for this are below.

When your resident part of the return is finished in TurboTax, print the return and write on top of the return, Dual Statement. 

Put the 1040NR on top of 1040 resident return and staple and mail to the IRS.  You must sign the 1040NR before mailing.  You do not need to sign the 1040 statement.

You will need to staple your 1040NR and 1040 together and mail to the following address:

If you  are not enclosing a payment then use this address...

Department of the Treasury

Internal Revenue Service

Austin, TX  73301-0215

USA

If you are enclosing a payment then use this address...

Internal Revenue Service

P. O. Box 1303

Charlotte, NC 28201-1303

USA

Please see more help on dual status returns see page 7 of Pub 519.

Publication 519

You must choose itemized deductions.  Please follow the below instructions to switch to itemized deductions.

TurboTax Online instructions

First, sign in and make sure your return is open. You should see 2018 TAXES in your left-hand menu as pictured below (if not, tap or click the upper-left corner to expand the menu or select Take me to my return).

Once your return is open:

1. From the left-hand menu, select Federal (on mobile devices, you might need to scroll down).
2. Now select Deductions & Credits near the top of your screen.
3. When you get to Now it's time for the fun part... Your tax breaks, scroll all the way to the bottom and select Wrap up tax breaks (if you don't see this button, select Skip to see all tax breaks, then scroll down again).
4. Continue through the interview until you see The Standard [or Itemized] Deduction is Right for You, pictured below.
5. On that screen, check the box Change my deduction to see the dollar amount for each deduction.
6. Select Continue if you want to save any changes. If you're switching to the itemized deduction, you may be prompted to upgrade.

So that means I can still take the full child tax credit (2000) or only in proportion (4 months divided by 12 months)? Also, can I use the Foreign Earned Income Credit for the part of year as a resident alien (I lived and worked abroad for the entire 4 months)?

Yes, you can take the full credit and you can use the foreign earned income credit on your resident portion of the dual status return.
 As a dual-status alien, you generally can claim tax credits using the same rules that apply to resident aliens. There are certain restrictions that may apply. These restrictions are discussed here, along with a brief explanation of credits often claimed by individuals.
EIC
You cannot claim the education credits, the earned income credit, or the credit for the elderly or the disabled unless you are married and you choose to be treated as a resident for all of 2018 by filing a joint return with your spouse who is a U.S. citizen or resident, as discussed in chapter 1.

I mean the "Foreign Earned Income Exclusion."

You may not take the foreign earned income exclusion as you were not a US citizen or green card holder when you returned to your home country.

I mean only for the part that I was a green card holder (4/12 months), can I take foreign earned income exclusion in proportion?

Can I take the child tax credit if I moved to the US from another country in September of 2022 with a green card for my whole family. So we were present in the United States for about 4 months.  If you moved here in Sept 22, then you would have been here for all 12 months in 2023 or did you leave the country for a while?  Or are you wanting to file 2022 taxes?

In order to claim the Child Tax Credit or EIC,  your children would have to have an SSN valid for employment.  

To claim the EITC, you would have to have been a US Citizen or Resident Alien for the entire year.  So, if you were only in this country for 4 months, you would not be able to claim the EITC for that year.  If you were in this country for all of 2023, and all of you have SSN's that are valid for employment, then you may be able to claim the EITC if you meet the rest of the criteria for claiming the EITC. 

Even if you claim US Resident status for the entire year, you would have had to be in the US for at least 6 months in order to claim the EITC. So having only been in the US for 4 months, you would not qualify.

Now, if you are working on filing your 2022 return, then you would need to download the 2022 version of TurboTax to file through TurboTax.  You cannot use the current version of TurboTax to file your 2022 return, you can only file your 2023 return using the current version of TurboTax.  

Rules for Child Tax Credit 2023

Who Qualifies for the EITC

You definitely meet the resident alien test if you have a green card under these rules. See HERE under Subcaption "Green card test requirements.

Being the fact that your child already meets the 1st requirement of being a resident alien by having the green card, there is no longer a substantial presence test requirement. As such, as long as your child lived with you for more than half of the year, you would qualify. See HERE  #4 and #5.