The main difference between them is that one of them is wrong; the other is grammatical, but not quite idiomatic.

This is incorrect:

It's the last time I've explained this to you.

"It's the last time" is present tense, while "I've explained this" is past tense.

It's the last time I'm explaining this to you.

This version is fine and might be something that somebody would say, speaking extemporaneously. However, if I was to write this, it would be:

It's the last time I explain this to you.

The main difference between them is that one of them is wrong; the other is grammatical, but not quite idiomatic.

It's the last time I've explained this to you.

This is incorrect, because "it's the last time" is referring to the present, while "I've explained this" is past tense.

It's the last time I'm explaining this to you.

This version is fine and might be something that somebody would say, speaking extemporaneously. However, if I was to write this, it would be:

It's the last time I explain this to you.