To show that any language $L \in NP$ is many one reducible to HP
In fact we can prove something a bit stronger: any language $L$ in NP is polynomial-time reducible to the Halting Problem $HP$.

So let $L$ be a language in NP.
We have a nondeterministic TM $N$ for $L$, which runs in polynomial time.
So
$$
x \in L \iff N \text{ accepts } x
$$
Now $N$ runs in polynomial time --- let's say that on input of size $n$ it runs in time $P(n)$, where $P$ is a polynomial.
Here is an algorithm reducing $L$ to $HP$:


On input string $x$, construct a Turing Machine $M_{x}$ which does the following: "Write $x$ on the input tape, then start trying all possible runs of $N$ on input $x$, in increasing order of size (first try runs of length 0, then runs of length 1, and so on). If a run ever accepts, then halt. otherwise keep running forever.


Now if $x \in L$ then there will be a run of $N$ on input $x$ that accepts, so $M_x$ will halt. And if $x \notin L$, then no runs of $N$ on input $x$ will accept, so $M_x$ will run forever. Thus,
$$
x \mapsto M_x
$$
is a reduction from $L$ to $HP$.
And you may also want to check that the reduction runs in linear time. (That is, the amount of time required to construct $M_x$ from $x$ is linear in $x$.)