Play as little TLA as possible. Skip everything that's not strictly required. Use memory corruption to trigger the epilogue without ever entering Mars Lighthouse.
The only restriction in this category is that you must not transfer data from the 1st game. This means all glitches and RNG manipulation are allowed.
Get Lash, get Iron, defeat the final boss, clear Gabomba (required to get the ship), do Fun™ things in Air's Rock, sail to Prox, win.
Regnetreis worked out the Air's Rock movement and the death storages. Plexa worked out the general route and the final boss. Random encounters were routed by me.
One character names are optimal. And ! in particular gives an optimal
Gabomba statue - the final puzzle is dependent on Felix's name.
Most likely the retreat glitch, which is triggered by casting retreat from a hotkey while having less than 6 pp.
Holding L trigger + Start while loading a game loads you into the last town you visited.
This is called death storage. By having a character die on the same frame as when you hit a loading zone, the loading zone won't trigger. This lets you go out-of-bounds.
Poison damage is used to trigger the death. The glitch is technically frame perfect, but there are setups that make this easy.
It only works on a few loading zones in the game. Thankfully, it works everywhere where we need it to work.
I'll let Plexa explain.
tl;dr: Standing on the floating tiles writes data to memory. Standing on out-of-bounds floating tiles writes data to unintended memory locations.