So can Human Paragon(1 gets you a single martial weapon, but you will want to take all 3), Arcane Archer(1 gives all martial weapons, you'll want 2 for the ability to use damageing spells with the better range from your bow), or Dragon Slayer 1(all martial weapons, armor up to heavy and shields except tower shield).
There might be more, but aside from needing to take Dodge(I'd recommend any other feat, that can count as Dodge) and paying for Iron Will(Otyugh Hole) Dragon Slayer is the simplest way to martial weapons, I know off for arcane casters.
The fluff-requirement(Kill a Dragon) is easier, than finding the hidden jungle temple of the couatls. If you meet him while you are Lvl 1, even a Kobold might suffice(It does count as a Dragon, as per the dragonblooded subtype). If not: Lesser Planar Binding, call Half Dragon Demon or Devil of appropriate CR, (de)buff at leisure, dismiss protective circle and slay it.