I often sign as Archer when I need to, but I'm not purely Archer. It is possible to reach one power through another, such as Brute through Changer, but there are some that are more "pure" and fundamental than others, without which one does not get very far.
Breaker breaks physics or the usual rules, and it's quite a power. You can reach it with Tinkering or Thinking, just as other technological / martial advances can be achieved with these two. The difference between Tinkering and Thinking is that Tinkering requires experimentation, and Thinking is more to do with pure logic, mathematics and sometimes "common sense".
Trump knows how to mess with powers, nullify or potentialize the powers of others. Some psychological intuition is necessary.