1. 该句是一个含有定语从句的复合句。

One way 是主语，is 是系动词，by becoming more and more specialized, with limited success 是表语。by doing sth. 表示做某事的“方式”。

红色部分是定语从句，省略了关系词:

One way scientists have tried to cope with this mountain is by becoming more and more specialized, with limited success.

还可以说：

One way that scientists have tried to cope with this mountain is by becoming more and more specialized, with limited success.

One way in which scientists have tried to cope with this mountain is by becoming more and more specialized, with limited success.

2. 定语从句使用现在完成时，说明try 的动作已经发生，跟主句的一般现在时的is 不矛盾。即便try使用一般过去时也不错，定语从句的时态跟主句不必一致或呼应。又如：

The book that you have bought (bought) is very instructive.