Your code as you have posted may not tell the entire story. Normally there is an interface (user constraints, thanks Bob) file that defines pin edge inputs and outputs to a port of a circuit internal to the FPGA you define. I am not seeing that.
Secondly, I also see in your code that you have 2 differing circuits driving each one of your output LEDs.
You have an if statement that checks for BTN_3 being 1, which will drive ALL of the LEDs to 0, then a set of If statements checking the input state of each "Switch_X" which individually drives a 0 or one to each LED. This is actually illegal. You can only have one circuit driving any output port.
What you should do is write this circuit as follows:
architecture Behavioral of Switch_led is
begin
Process(Switch_0, Switch_1, Switch_2, Switch_3, Switch_4, Switch_5, Switch_6 , Switch_7, BTN_3)
begin
if BTN_3 = '1' then
Led_0 <= '0';
Led_1 <= '0';
Led_2 <= '0';
Led_3 <= '0';
Led_4 <= '0';
Led_5 <= '0';
Led_6 <= '0';
Led_7 <= '0';
else
if Switch_0 = '1' then
Led_0 <= '1';
else
Led_0 <= '0';
end if;
if Switch_1 = '1' then
Led_1 <= '1';
else
Led_1 <= '0';
end if;
if Switch_2 = '1' then
Led_2 <= '1';
else
Led_2 <= '0';
end if;
if Switch_3 = '1' then
Led_3 <= '1';
else
Led_3 <= '0';
end if;
if Switch_4 = '1' then
Led_4 <= '1';
else
Led_4 <= '0';
end if;
if Switch_4 = '1' then
Led_4 <= '1';
else
Led_4 <= '0';
end if;
if Switch_5 = '1' then
Led_5 <= '1';
else
Led_5 <= '0';
end if;
if Switch_6 = '1' then
Led_6 <= '1';
else
Led_6 <= '0';
end if;
if Switch_7 = '1' then
Led_7 <= '1';
else
Led_7 <= '0';
end if;
end if;
end process;
end Behavioral;
What I have essentially done is to bring all of your individual Switch_X checking into the else clause of the btn_3 check. This forces what I was stating before, that only one logic circuit will drive any LED at any point in time.