7D Jogging 1H, 6D Snooker 2H + Job

Many years ago, I have tried continuously joggingto go jogging every day for a month.

"continuously" is a little too much here, it sounds a little like you wanted to jog 24 hours a day for 30 days. And present perfect "have tried" doesn't really seem to fit.

At the end I only missed one day.

Past tense for this too.

TAt that time I doidn’t have a job.

And past tense again.

Last week I have tried continuously jogging for one hour each day.

"for one hour each day" means "continuously" works much better here, it's now clear you just mean jogging for an hour without a break. And present perfect "have tried" is good. You could also use present perfect progressive "I have been trying to jog".

This is clear and understandable without "for", by the way, it just sounds better with it!

I completed the week!

This sounds really weird and vague - you need to say what you completed.

Physically it is no problem at all.

Or "it's".

The hardest part is how to mentally overcome this task.

"how" here needs a to-infinitive. Like I don't know how to drive a car, I will teach you how to bake this cake, this book explains how to identify birds.

It would be a little more natural to use a gerund: "The hardest part is mentally overcoming the task."

Anyway, finisheding this task giave me a lot of confidence to face my next challenge.

Here you really need the gerund, or something awkward like "The fact that I finished this task gave me". I changed to past tense "gave" but you could also say "gives me a lot of confidence", which would focus more on how you have the confidence right now - but "give" is wrong.