In the project they use Arduino Uno but i cant. I need to use just microcontroller ATMega328p.
BUT I dont know if the project is caunting on components already build in arduino or not.
If YES does that mean i need to rebuild the whole arduino on to a bread board or just some part of the arduino. Or is there smarter way of executing it ?
If you don't have a need to upload code via USB and no need for serial communication with a PC, you can leave the components that relate to it out; that is the 16U2 and related resistors/capacitors/crystal. You will have to upload via ICSP.
If you don't need the led on pin 13, you can leave that part of the circuit out.
If you only want to power it with 5V, you don't need the voltage regulater that converts Vin/barrel voltage to 5V. The circuit also does not show the use of the 3.3V power so that can be left out as well.
//Edit
Breadboards are not really useful in "violent" environments; wires can come loose easily and it suffers often from bad contacts. Consider soldering your circuit on perfboard after a breadboard prototype has provento work.
Are you suggesting to use a bare chip to build your first prototype?
You would need to build some things around it. At least oscillator capacitors, and capacitors from plus to ground.
Not recommended as a newbie project.
Depending on the package of the chip, soldering can be quite difficult.
Debugging will be very challenging if you have at least 3 things that can go wrong...
Loose contacts
Bad program
Bootloader issues
Buy uno or mega and get it working....
That way you can be sure bootloader and connections are ok. Run blink example first. That way you know all other problems come from things you added.
...if form factor is unhandy (too bulky) look for Nano...