Achieving goals like opening a business, buying a home or going on
dream vacation, require a basic method of savings to make it
My question is is this verb form correct? Or should it be requires instead?
What’s the grammar topic here? Please explain.
The subject of this sentence is “Achieving goals”, and it is singular. The examples you mention do not make your subject plural. Therefore, it would be “requires”. This is subject-verb agreement but should also fall under the gerund (achieving is a verb that operates as a noun) category.