How to parse and translate 必须要有?
ABC dictionary defines 要有 as

V.
need; require

giving the example:

开箱子要有钥匙。
Kāi xiāngzi yàoyǒu yàoshi.
One needs the key to open the suitcase.

必需 you can think of as essential, indispensable or necessary.

Your translation:
人必需要有自己的追求， 'a person needs must have a pursuit'
while not wrong - could probably be better thought of as definitely necessary instead.