How do I Keep Piling on the Debt?

I regret having been unable to unlock this before the very last quest: Q77. ABYSS.

The rest of this answer spoils that quest, plus items and allies unlocked by then.

While a strong party is likely to help, I could do this with just Sasha in my party. Of course, unlocking Sasha is not very simple, but the default Destiny team should do just fine.

For equipment, I used the Goddess Book found in Q77 itself, which features reduced knockback with respect to (say) the Destiny Sword; the Brave Guard, the Mighty Protector, the Brave Crown, the Destiny Boots and Full Break put me overall at 999 health, 492 attack, 457 defense, 188 speed, 90 weight and 36 critical while on global time. My global level was 118 (your life will be somewhat easier in this quest if you wait until global level 120); I do not recommend attempting Q77 at a lower global level. For reference, with this setup you should be able to take down the "statue heroes" on the map by dashing against them at about level 252 or so. If you care, I used Hero as my class.

What makes it easier (possible?) to deal with the debt cop in quest Q77 was, of course, the Goddess Porta-Statue sold in the southern village. The rough outline of the quest is:

• Avoid the blinking red enemies
• Get money by fishing in the southeast corner (you can do this arbitrarily many times)
• Use the time you just bought yourself to get to level 120 if you aren't there already
• Grind money from the right demon (you can heal for free and rewind time anytime there)
• Grind money from the right and south demon
• Grind money from the right, south and left demon
• When you hit level ~180 switch to grinding off the two northern group of monsters
• Make sure you do buy that Goddess Porta-Statue
• When you hit level 255, use the caves to get to 99,999 gold, then move to the center village
• Reset time and borrow money
• Dash straight north and confirm you want to face the goddess
• The debt cop will come knocking.
• Simply lay the controller down and, when the time has almost ran out, hit X to reset time.

After about 40 seconds the bird cop should go down and your achievement should be unlocked. I also managed to beat the goddess in the remaining time by dashing into her.