Osaka is known for its food culture. If there's any place next to Tokyo where you can find all kinds of Japanese specialties, it's here. The city is full of life, music, street culture and delicious (local) specialties on every street corner. While almost all of the food looks delicious, the majority contains animal products or meat, and is therefore not vegan. However, I've found three awesome restaurants in the hustle and bustle of Osaka-life that offer some great options for eating Japanese food.
1. Tempura Daikichi
Tempura Daikichi is a very popular tempura restaurant in the center of Osaka city. Traditional tempura is fried vegetable/fish/... in a batter of rice-flour and water. I believe Tempura Daikichi doesn't use egg in the batter, but it won't hurt to ask to be sure. While the restaurant has many non-veggie options, there's also a big range of delicious vegetables on the menu. And the great thing is, you order by plate. So you can just try a couple, then try some other ones, and maybe have some more until you're totally full and can barely walk away anymore haha.
One reminder though, the sauce that comes with the tempure usually contains dashi (fish stock), so try to ask for some simple soy sauce if it's not on the table.
2. Shizen Bar Paprika Shokudou Vegan
Shizen Bar Paprika is an entirely vegan 'shokudou' (which means canteen in Japanese). It is, however, a really nice cute restaurant that kind of looks like you could find it in the hidden streets of Paris. They work with organic food, raw food and macrobiotic cooking and their menu offers absolutely delicious options both Japanese as well as other things.
3. Green Earth
Green Earth is another restaurant with mostly vegan (and entirely vegetarian) options. Their restaurant is in the city center and offers delicious food for reasonable prices. They have both Japanese, as well as more European-ish options and even make vegan cheese (OMG YUMMY <3). Definitely have some lunch here if you're out shopping for a day around the city center!
(I believe it only opens for lunch, so until around 16:30. But on Friday it seems to also be open for dinner 18:00-21:00)