How would I do this? What could my weekly shopping list be?

Eggs
Chicken
Load up on green veggies

Be willing to stick to routine meals if $25 is your budget.

Drink lots of water.

it's hard to budget while doing atkins but it's not impossible.
This is what i do:
-check out all the sales at the grocery stores.
-cut Cut CUT coupons for items that are on sale (ie, two bags of salad are on sale for $5 and i find a coupon 25% of coupon on salad)
-check out your local farmer's market for sales and stock up
-have a list of items that are on sale and try to stack coupons on sale items (store coupons and newspaper coupons can be used for same item)
-be prepared to eat the same routine meals
Good luck and let me know how it goes

Butter
Eggs
Cheese
Chicken
Frozen veggies (usually cheaper)
Jar of salsa