Notes from author
As an SL 1 invader, killing your target is largely trivial, assuming you're willing to stoop to things like using a maxed out Pyromancy Hand with Great Combustion. As such, your primary goal should not be elimination, but intimidation. And what better way to intimidate than to confront a starting player as the final boss of the game?
Unfortunately, with your shitty Dexterity, the only sword (and I use this term generously) you can use is the Broken Straight Sword. Naturally, you should go with the Raw upgrade path for maximum pro cred. Just apply a Charcoal Pine Resin and you're the spitting image of the Lord of Cinder himself! Well, kind of, anyway.
Your primary strategy should be to play mind games with your victim, poisoning them with Dung Pies (and slotting in Poison Throwing Knives should you get the opportunity), stopping them from healing with Lloyd's Talismans, and hoping they'll panic, blunder into a group of enemies, and die. Attack with Firebombs and the Great Lord Broken Straight Sword whenever you feel you aren't being taken seriously. Fire Surge and Fire Tempest are solely for pyrotechnics; use a base level Pyromancy Hand if at all possible. The Fire Light Crossbow should only be used in case of emergencies. (Or gankers.) (Or Darkmoons.) (Fuck Darkmoons.)