Hi, protein isn't the one and only nutrient to rule them all, so I'll make it short for you:
As a vegan you will have to supplement this vitamine:
You may also want to supplement (especially if you live in a country where the sun only raise low upon the horizon in the winter):
As a women you may eventually want to supplement:
I guess it may also be safe to supplement some:
When it comes to the proteins as long as you get plenty I doubt it's that important how perfect they are, for protein synthezies most of what is used is what have been broken down earlier, kinda everything will more or less get wasted anyway and not build new muscle and since you are consuming lots of it I doubt it's that important that you don't get to little of some amino acid vs if you ate very little protein. You don't really need to think much about it, legumes and grains usually complement eachother very good so as long as you eat a varied diet you will get both.
http://www.nutritiondata.com/facts/cere ... sta/5710/2
As you can see there brown rice got an amino acid score of 74 and is low on lysine, you can also click a link to find foods which complement rice.
http://www.nutritiondata.com/facts/legu ... cts/4435/2
Chickpeas, amino acid score 106, high in everything.
http://www.nutritiondata.com/facts/legu ... cts/4424/2
Kidney beans, amino acid score 103.
http://www.nutritiondata.com/facts/legu ... cts/4455/2
Soybeans, amino acid score 116.
Oh, fuck this, I don't seem to find what I was after for. Anyway yes I think grains use to be low in lysine and legumes in methionine. (And eventually quinoa are rich in both, or if it was just rich in what soy is comparable low in.)
Anyway, eat various sources and you won't have to think about it, it will be harder to get loads of protein though. You can always supplement with a concentrate/isolate or free form essential amino acids.
And when it comes to fats most vegetarian fat sources have loads of omega6 in them but you would be better of with balancing that with omega3. So either you can eat flaxseed oil and choose nuts with a decent omega3 to 6 ratio such as rapeseed and olive oil or you can try to limit your omega6 intake by for instance using olive oil which has loads of omega9 instead. You could also supplement with vegetarian DHA capsules if you want to.
Regarding athletes I assume some may just eat a very clean and healthy vegetarian diet and then call it whatever, and they can also take supplements, and in the case of world class athlets some of them probably take drugs.
He don't look huge either.
And btw, remember, the more you move around, the more energy you need to consume, and the more you will eat. The more you eat the more protein and other nutrients you get with your food. So risk of deficiency probably goes down with a more active life style, not up.
Phelps claimed he ate 10.000 kcal / day or something such, and he probably consume a hell of a lot of energy swimming for hours a day, with requirements like that it's ok for him to eat lots of pasta and energy drinks, and even if his diet looks shitty he may get enough vitamins and so on anyway since he eat so much of that less nutrientdense food.
Good luck and don't worry too much. Eat lots of beans, get your vegetables, fill up with nuts, grains and fruits for the rest of your requirements. Supplement if needed.