First of all, this section is used for showcasing games that you've made, not for asking questions. Also, I'm not a lawyer and a quick Google search would answer that question for you.
In general, no, it's not legal. Especially with big companies, like Nintendo and Sony, that very aggressively protect their IP. Some indie devs don't care and do it anyway. But, once your little game becomes popular and gets the notice of said companies, you're going to get shut down, sometimes with legal consequences. However, Sega has given their OK to certain games in the past. You might want to send them an email and ask them first since Alex Kidd is their property.
My question to you is "why would you want to do that?" If you can recreate the mechanics of the game, why not just use your own artwork? The Alex Kidd character is a fairly simple design. I've also seen plenty of free-to-use assets that are much nicer looking.
You're better off just playing it safe. ;)