Question

帮忙看看有没有语法错误

i just found out that to be eligible to become a licensed architect, i will need to have completed the master course

Answer 1

有三处语法错误

...... a licensed architect, i will ......
这里不能加逗号。这里的句意是连贯的，没有插入语存在，不加逗号。反过来考虑你会更清楚：I will need to have completed the master course, to be eligible to become a licensed architect.这里的逗号显然不应该有。

...... I will need to ......
因为你前文用的是found out过去时，这里应该是 I would need to

...... need to have completed ......
to have completed是不对的。没有need to have + pp. 的用法，改为 need to complete

除此之外，改进建议：
I would need to 直接用 needed to代替，意义不变。
to be eligible改为to be qualified更合适，因为qualify直接指出，有一个衡量标准

found out在这里是对的，found也是对的。

Answer 2

i just found that to be eligible for a licensed architect, i need to have completed the master course。
附：found out有“找出证据”的意思，用found 就有“发觉”的意思。