2 is correct but can anyone explain why 3 is wrong in this case?
The most important restriction regarding the use of -고자 is that you need to use the same animate subject before and after it (Note: This animate subject includes an individual, a group of people or animals, an institution, a country, etc.). I cannot tell you why, but this is how people use it.
The preceding part of that sentence has "you" (or "I" or "we") as the subject, whereas the following has "철저한 계획과 꾸준한 노력" as the subject. Therefore, the sentence has the two subjects and the following has an inanimate one.
If you wish to use 달성하고자, you have to rewrite the following. For example, it is correct to say "목표를 달성하고자 한다면 철저한 계획과 꾸준한 노력을 해야 한다." because it has one animate subject, "you" (or "I" or "we"), but it is better to say "목표를 달성하고자 한다면 계획을 철저히 하고/세우고 노력을 꾸준히 해야 한다."