Assuming female, 5'5", age 35, somewhat active because it's more conservative; daily caloric intake is like 1700. Your egg macros are about 5.5g of protein and fat per egg for about 72 calories per egg. A large egg is 7g protein, 7 fat. 91 calories. My math is based on large eggs, 9 cal/g fat, 4cal/g carbs and protein. To get all of of their caloric intake from eggs would be around 18 eggs.

Vitamin A in eggs is 75iu, 23ug RAE. RDA is 700ug for this person. 30 eggs. The tolerable upper limit is 3000ug. 130 eggs.

Macros: 126g of both fat and protein. Carbs in eggs are negligible at maybe .5g each, totaling 9g or 36 cal. Harvard recommends .36g/lb for protein, which is about 40g. They also set the theoretical upper limit at 2g/kg ; .91g/lb, which is 102g. So this is 24g excessive (3.4 eggs). The quantity of too much protein is debatable, though in the absence of heavy weight lifting, this is at least excessive for most people. Harmful depends on context.

126g of fat is 1134cal. This is below what they need to maintain weight (calorie deficit) and the biggest problem with this diet so far. If this person are more than 150g of carbs per day, I would be concerned because with circulating glucose, body fat is not used readily to supply caloric need. The body may want to use protein as a calorie source, which is where the danger of eating too much protein comes from.

After being on this diet for several weeks, they will be in ketosis, which will actually make it much safer. Body fat is used more readily in ketosis to fill energy needs and could make up the 600 calorie per day deficit, totaling to a little over the safe 1lb per week recommendation for weight loss.

I would advise adding more fat and reducing protein a bit (80g should be plenty though potentially excessive still), not because this is dangerous but because it is excessive and the body will need to remove the excess protein as waste. This isn't really harmful in smaller quantities but does put more strain on the kidneys.

Maybe 12 eggs a day and another 50 of mostly fat to get 500 calories, 500 deficit. If trying to maintain weight, increase fat by another 50g. Mix carbs if you want under 300 calories (75g) with that amount removed from fat intake and preferably in one meal with protein.

Doesn't consider vitamins other than A.