there be 结构做定语从句也没什么特殊的知识点.这句理解为省略了that 就可以了:
It's self-evident that no one would have time to know everything (that) there is going on in the world.
定语从句部分完整的说法应该是:
There is everything going on in the world.
其中going on 是修饰 everything 的 分词短语.
放进原句中意思应该是:
没有一个人有足够的时间去了解所有存在于世界上的正在进行中的事情.
翻译得蹩脚了些,但感觉用上了"there be"之后就强调“存在”的含义.