This is, of course, a matter of personal opinion to a large degree. All countries face challenges and it is hard to say which challenges are objectively more serious.
If we are using the term “Pacific Realm” to include all of the countries in the Pacific, I would argue that the small countries of Oceania face the greatest number of challenges. The countries that face the most challenges would be small countries that have many atolls and are relatively isolated geographically. A good example of this would be the Marshall Islands.
Isolated countries face economic and social challenges. These countries have very little in the way of natural resources. Their isolated locations make it very hard for them to attract tourists. Countries with very small sizes do not have the land or the labor resources to be attractive as places for manufacturing. This makes it hard for them economically. Socially, they face challenges because their old ways of life are no longer feasible when their people know about and want modern lifestyles. This leads to challenges as they try to change their ways of life to adjust to the new realities. Countries with many atolls face particular challenges due to global warming. If sea levels rise, these countries may lose much of what little land area they have.
For these reasons, I would say that the small, isolated countries, particularly those with atolls, face the greatest problems.