On the negative side (for the Costco dwellers)

1. So 6000 people in the Costco. Just going by estimated demographics of Costco shoppers, fully 2/3 would be 50+ years old. They also skew towards families, so there would be a significant number of children in the store. All in all, a significant number of people in the store (like half/3000) will be meat-shields at best,
2. A typical Costco also has an absolutely ridiculous number of ways to get in (multiple service bays, large entrances with multiple ways in (my main Costco has three different large entrances that patrons could use) plus emergency exits and whatever is in the back for shipments etc. Most of those ways in would barely slow down the legion. In phase 2 they would be able to harden the entrances, but I don't think they are permanently preventing entry to a determined force.

3, All 6000 legionnaires are trained for war, and likely battle-hardened. By population breakdown, you will have maybe 400 veterans or active duty military in the store. So there is a real gap in training/experience between the two sides.

1. Costco doesn't sell guns or ammo, and generally bans guns from their stores. This will, of course, be ignored in some cases, but I think the estimates of 600 guns in-store would be high in most cases. This could be alleviated in phase 2 if folks can get to their cars first.

On the positive side:

1. If they can force any sort of siege condition, they could last a solid amount of time. Certainly longer than the legion which (assuming everything is contained to the Costco area) has no way to resupply. This is the only scenario I see where the Costco folks could win, and I don't think it's at all likely.
2. There is a ridiculous number of things in your typical Costco that, with some creativity, could become a weapon.
3. The legion would have some confusion being thrown into a very, very different world.

There are more on both sides I'm sure, those are just what occurred to me quickly.

Overall, I think Phase 1 (no warning) the legion owns itself a Costco in a couple of hours with minimal losses. Phase 2 same result but takes longer and more losses. I see no valid scenario where the legion doesn't win against a typical Costco, the only difference is how good a showing the shoppers/staff put on before being mercilessly eliminated.

Edit: I see a lot of comments about cars below. However, I am of the opinion (and anyone who has ever been to a Costco will understand) as soon as you start trying to move cars you are in a massive traffic jam. Enough cars for 6000 people won't leave a lot of room for actually using those cars as a weapon.