How do you get SSS rank in Egg Heist?

You need both conditions at once: the loot value and the eggs. Hitting one without the other drops the guarantee. A backpack full of loot with a single egg is not a sure SSS, and neither is two eggs with thin loot behind them.

How many eggs? Two is the number to plan around. In practice that means grabbing the central egg, which twines you with it and turns you into the egg on the way out, then finding a second before you head for extraction. If you need your hands free to deal with something, press C to untwine. The egg stays where you set it down, it is not forfeited, and you can pick it back up.

For the value side, be picky. Gold-tier items and talent materials are what push the total toward 500,000. Filling the backpack with everything you pass gets you there slower.

Chaos mode is looser at the bottom end

Chaos Egg Heist lets you extract without any egg at all, as long as you carry a minimum amount of loot value. An extraction there with a score just over 500,000 can still earn an SSS. So the lower end of the value range is enough in Chaos, but the guaranteed route is still the same: clear the value bar and bring two eggs out with you.

Not settled: The exact cutoff is not fixed at a single number. The 500,000 to 600,000 range is approximate, and a Chaos run just over 500,000 has landed SSS, so the real threshold may sit nearer the bottom of that range.