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I'm using an Asus B250M motherboard. I found it has so many BIOS update files. Their versions are denoted as 12xx, 11xx, 8xx etc. Each update description says it is for a specific purpose.
I'm obviously using an old one which I thought will be the only update. But I see the manufacturer released more over time.
So should I install the only current update or all of those as they were released chronologically? Sadly the manufacturer has no instruction about which BIOS update to install.

There's no guarantee that you can successfully install the latest available BIOS/UEFI update and have it work. In many cases, a manufacturer will release a BIOS update that requires the motherboard to already have been updated to a certain version level before it can be installed.

For example, BIOS version 99 may require version 35 or higher. In this case, if you have version 27 installed, you would first need to update to version 35, then you could safely upgrade to version 99 (skipping all the versions between 35 and 99).

Sometimes there other unusual requirements for installing these updates. In fact, while searching the Asus site for info about your board, I ran across this, which doesn't apply to your board but demonstrates my point exactly:

If your BIOS Version of ASUS 100 series MB is under 1800, and you want to upgrade BIOS to support the latest 7th Intel CPU, please do remember to update BIOS two times to 30xx version manually.

(emphasis mine)

Only the manufacturer knows of these dependencies. They should be clearly stated in the release notes for each BIOS version.

If you cannot obtain this information, then you should install each update from oldest to newest. Since this is the order in which the updates were released over time, you will not run into any dependency problems.

Your specific case:

I searched and could not find any BIOS release notes on Asus' site for your motherboard. However, Asus provides the AI Suite III application which includes EZ Update. According to the manual for Asus PRIME B250M-A motherboard:

EZ Update is a utility that allows you to automatically update your motherboard's softwares, (sic) drivers and the BIOS version easily.

In my experience, tools like this one are aware of any dependencies and will guide you through installing the updates in the correct order.

You can download AI Suite III from Asus' website here.

So should I install the only current update or all of those as they were released chronologically?

In the time of Spectre and Meltdown, you should update the BIOS to the latest version. This will surely slowdown your machine, but, at the same time, increase your security from these attacks.

The only argument against BIOS updates

If it ain't broke, don't fix it

does not apply in the age of Meltdown and Spectre.

Nearly all current Mainboards do need an update in this regard.

He, who claims otherwise, has no idea of what's he talking about.

So, final answer:

Update your BIOS to the latest version.

If it ain't broke, don't fix it is a sound principle for BIOS updates. If you were facing a particular issue which a BIOS resolves, then it's time to think about updating it.

However, a security issue does exist, and all BIOS versions dated 2018/03/26 or later will include the CPU Microcode patch, so I recommend updating, starting with the version just barely newer than what you have now, applying each update in series, until you have completed the install of Version 1205.

There's also a security fix to the Management Engine, which is different than the BIOS, and I recommend updating to Version 11.8.55.3510; again, from the version you have now, one at a time in series, until you have applied the latest.

Both are obtained from the same download page.