Does anybody remember the NES game Crystalis? I loved that game. I wonder if it would be possible to remake it??

Yes, it was a fun game. It's on the Switch's virtual console and the PS4's “SNK Collection” right now if you want to play it.

You cannot remake it legally unless you work with SNK as a port or by giving an enormous pile of cash to license the property.

Attempting an unauthorized remake is a great way to be sued into oblivion. They generally end with settlements (where you beg for legal mercy) that include gag orders preventing you from talking about it, other than warning others that it's a really bad idea.

You could make a so-called “spiritual successor”, following story themes or gameplay elements but being careful to stay away from copyright issues (don't use their assets, names, scripts, or music), from trademark issues (don't use their names or distinctive, recognizable elements), from trade dress issues (don't use their color combinations, visual styles, or layouts), along with other IP issues.

Making a top-down RPG Action game with early-90's style pixel art is fine. Making a story world with four mystical swords each with a special ability is fine.