As a Concept artist, you have to show artworks that an Art Director can use for the job, at the end of the day it's business, and you have to sell ideas with your skills. If you want to do Creature design, then show creature work like full creature standing in an environment, do portrait studies with eye variations, textures variations, or place your creature in different lighting conditions.
Show that you know anatomy, it is also critical to have the fundamentals of lighting, and perspective done correctly.
Whether you are doing environment or character, you need to get your fundamentals right. For that you can go on the internet, there is all sorts of materials for free or online schools that you can attend for a few bucks a month.
Software is easy to learn; you have to spend some time on them to get a decent level of experience. What's most important is to get an eye for good design. It can take years to train your eye. Having a good taste for colours or shapes need more practice.
Tools are just tools that you use to show your visions. These days things are pretty fast moving, and software is constantly evolving, so you have to evolve with it, sometimes a tool can make things much easier.
If you want to go for character/creature design you have to know ZBrush, Photoshop, and Keyshot. They will make your creative process much easier and faster.
Why ZBrush? Because once you have a sculpted creature, you can rotate around and have different views for free. Usually, a client will always look for that kind of extra level, and once the client is happy with the broader shapes, you can even do textures studies and then show that model into Keyshot and play with different lighting conditions.
These days, with the importance of the internet, your portfolio represent who you are, so take good care of it and get your work out there. Website like The Rookies are an amazing place to start.
Always remember it's better to have five killer artworks than 20 artworks with an average quality. And always look for the quality and push your creative and technical limits.
If you do all this and take your time, you will get where you want to go!