[Android Q&A, Help & Troubleshooting] c627627:
I have achieved success but do not exactly know how.

If I had another identical phone, I would retest this but I do not, so another user needs to take over and verify this and change what needs to be changed. I will post everything I did, some of which is unnecessary, I don't know which parts worked but this is what I did and hopefully it will help people. :)

0. Install link2sd although I do not think you need it, but some people did:

https://play.google.com/store/apps/details?id=com.buak.Link2SD&hl=en

1. Download KingRoot5 but do not install yet:

hhttp://xdaforums.com/devdb/project/dl/?id=21707

2. Download and install Terminal Emulator:

https://play.google.com/store/apps/details?id=jackpal.androidterm

Download and install the latest version of Root Checker:

https://play.google.com/store/apps/details?id=com.joeykrim.rootcheck

3. Download SuperSU, which I believe can only be installed after you are rooted with KingRoot.

Do not run or update it yet!

https://play.google.com/store/apps/details?id=eu.chainfire.supersu

4. Download and unzip "Replace_Kingroot_With_SuperSU.zip

http://tiny.cc/fo78zx

link courtesy of this xda thread, our thanks go to posters there: http://xdaforums.com/a310/general/how-to-remove-replace-kingroot-kinguser-t3308989

Extract folder mrw from that .zip file so that folder mrw is in the root directory of the internal SD card. I also placed folder mrw in the root directory of my external SD card.

5. Run KingRoot 5 scroll down and start the process, tap on Try Again button when asked.

Use the latest version of Root Checker to confirm you are rooted.

No need to reboot. If you would like to remove KingRoot and replace it with SuperSU:

6. Open Terminal emulator and type:

su

Allow root permission

then type:

sh /sdcard/mrw/root.sh

(Note that there is a space after sh)

7. DO NOT REBOOT.

This next part is confusing, I did not do this but others did, read BEFORE DOING ANYTHING:

This is a part where ordinarily bombardment of messages about KingRoot being stopped begins.

You are forced to TAP on OK all the time.

So you have a few seconds then need to TAP on OK. You need to take it easy and not get frustrated and use the few seconds between tapping on OK to start link2sd and use three dots in the upper right corner to search for King and tap on KingRoot and use the same three dots to select Uninstall.

I on other hand, installed SuperSU after being rooted with KingRoot but BEFORE running the script to remove KingRoot from here:

https://play.google.com/store/apps/details?id=eu.chainfire.supersu

And I did NOT run SuperSU yet.

8. Root Checker reported the device as UNROOTED because KingRoot is removed, however I NOW manually started SuperSU and it did asked to be updated and I did select NORMAL.

After I ran root checker, I manually started SuperSU and all of a sudden it only then ASKED me to allow root access for Root Checker.

Only then did Root Checker confirm that device is rooted and KingRoot appears to be gone.

Any clarifications should be posted by people who tested all this on a new Alcatel Ideal 4060a.

If I had another one I would figure out what worked, and what did not.

But I can't tell if link2sd is really necessary.