Weakness Order

This page is something of a troll, but it is true.

Neptune > Mars > Venus > Jupiter > Saturn > Mercury > Pluto > Uranus > Terra > Neptune

Bolded robots are in the second half of the game. As such, it is true you cannot use only weakness order.

Other Weaknesses

Dark Moon: Mars

Enker: Buster Only

Quint: Mars

Punk: Neptune

Ballade: Mars & Venus

Fists: Neptune

Wily Phase 2: Terra

Sunstar takes 1 point of damage from all attacks (Jupiter lasts long enough to hit twice)