Matching several things using a regex is pretty straightforward:

/(foo).*(bar).*(baz)/

This also implies the order of the things. If you want to require that foo, bar, baz all exist but in no particular order, you can use lookahead and lookbehind (explained in great detail in this wonderful regex tutorial article):

/(?=.*foo)(?=.*bar)(?=.*baz)/

If you also want to capture the things:

/(?=.*(foo))(?=.*(bar))(?=.*(baz))/
/(?=.*(?<one>foo))(?=.*(?<two>bar))(?=.*(?<three>baz))/

Let's see how that works:

for ("foo bar baz", "foo baz bar", "baz bar foo", "foo bar") {
    if (/(?=.*(foo))(?=.*(bar))(?=.*(baz))/) {
        say "'$_' matches the regex, \$1=<$1>, \$2=<$2>, \$3=<$3>";
    } else {
        say "'$_' does not match the regex";
    }
}

We'll get:

'foo bar baz' matches the regex, $1=<foo>, $2=<bar>, $3=<baz>
'foo baz bar' matches the regex, $1=<foo>, $2=<bar>, $3=<baz>
'baz bar foo' matches the regex, $1=<foo>, $2=<bar>, $3=<baz>
'foo bar' does not match the regex

Note that, obviously, the order of the captures follows the order it is defined in our pattern and not the order in the string that is being matched.

As a bonus, in this case the unordered version is faster than the ordered version because of reduced backtracking:

% perl -Ilib -MBencher::Mark=:all -E'$str = "foo bar baz";
  cmpthese(0, {
    ordered   => sub { $str =~ qr/(foo).*(bar).*(baz)/ },
    unordered => sub { $str => qr/(?=.*(foo))(?=.*(bar))(?=.*(baz))/ },
  });'
+-------------+-----------+-----------+------------+---------+---------+
| participant | rate (/s) | time (ns) | vs_slowest |  errors | samples |
+-------------+-----------+-----------+------------+---------+---------+
| ordered     |    860000 |      1200 |        1   | 1.7e-09 |      20 |
| unordered   |   2700000 |       370 |        3.2 |   1e-09 |      21 |
+-------------+-----------+-----------+------------+---------+---------+

And it becomes even relatively faster the longer the string:

% perl -Ilib -MBencher::Mark=:all -E'$str = "foo".(" "x10000)."bar".(" "x10000)."baz";
  cmpthese(0, {
    ordered   => sub { $str =~ qr/(foo).*(bar).*(baz)/ },
    unordered => sub { $str => qr/(?=.*(foo))(?=.*(bar))(?=.*(baz))/ },
  });'
+-------------+-----------+-----------+------------+---------+---------+
| participant | rate (/s) | time (ns) | vs_slowest |  errors | samples |
+-------------+-----------+-----------+------------+---------+---------+
| ordered     |     20000 |    51     |          1 | 1.1e-07 |      20 |
| unordered   |   2540000 |     0.394 |        130 | 2.3e-10 |      20 |
+-------------+-----------+-----------+------------+---------+---------+

But of course remember that separating the check into multiple simpler patterns can be even faster.