Is it possible to create a TBS for RPG Maker 2003 just like in the picture. (:3 My first post)

I'm pretty sure that would be one heck of an eventing nightmare.
Though I don't believe it would be impossible, I do believe that it is completely impractical.

There was once a game created in RPG Maker 2000 using a TBS (link), and here is another site where someone was recently developing such a system for RPG Maker 2003.

You can also find some interesting stuffs on YouTube in relation to this idea.

It certianlly is possible, but you need a massive amount of knowledge with programming, variables, and switches. And there will be so many conditional branches linking off to eachother you could re-design your family tree.

If you are going to create this you need a massive amount of time and knowledge on your hands. It is truly a shame that RPG Maker 2003 doesn't support scripts, otherwise this'd be a distant problem at the very least.

The problem is with TBS's is that if you are using custom damage variables and parameters. And spell damage is stored in a switch, branch AND variable for that matter. Meaning that for a proper / big TBS game we're looking at roughly 8000 Switches / Variables and many many branches. I remember assisting a friend of mine with a TBS once, for a single battle he used 231 Switches, 311 Variables, and I needn't count the branches...

Tackle this as you may, I can't really offer any help here, but it ceritanlly isn't impossible, it just requires a handful of word and dedication.

Possible? Very much so: Video of prototype.

The thing is that you need to know quite you're way around coding in events to do so. But unless you'd just use a pre made script, you'd still need the same knowledge of the concepts to make a script out of it.
The biggest difficulty with creating a TBS is making a reasonable enemy AI. For it to be reasonable, it needs to be able to find it's way around obstacles (both from the static terrain, and the dynamically positioned enemies), and you might want different terrains to cost more to travel (like woods in advance wars). And there's the issue of who the enemy should choose to attack, how to position itself if it's a long range unit, how to position the attack itself if it's an aoe attack and so on.

To give you a better idea at the complexity of making a "reasonable" TBS in rm2k3 you could take a look at these 2 tutorials:
TBS part 1
TBS part 2

And there are still two more parts to come before the tutorial series is complete and can construct a full TBS.

If those tutorials look like a bit too much or hard to grasp, but you still want to learn how to do it in rm2k3, then you should probably try coding something simpler first, like a custom menu system.