I do not believe it is possible, nor advisable, to teach all of the Algebra syllabus content for HL in one teaching unit. It's not just the issue of quantity (recommended teaching hours are more than 3 times that for Algebra topic in SL), but also an issue of items which do not require being taught together - e.g. Proof by Mathematical Induction can easily be taught elsewhere. Different to what I suggested for Maths SL, I suggest teaching a Sequences & Series unit that covers the content in syllabus section 1.1 (arithmetic & geometric sequences/series) but does not cover any of the other syllabus sections in the Algebra topic. The remaining content in the Algebra topic - binomial expansions, binomial theorem, combinations & permutations, and proof by induction - can all be covered in a separate teaching unit (Counting Principles; Binomial Theorem; Induction). As with SL, it might be best not to cover questions on sequences & series that will require logarithms to solve. It is not completely out-of-bounds, but the unit covering exponential & logarithmic functions will be taught after sequences & series. Certainly HL students should know enough about logarithms prior to starting the course to apply them in the context of sequences & series - but I would advise waiting to pose these kinds of questions during the exponential & logarithmic functions unit. It also serves as a nice review of sequences & series at a later time in the course.

The phrase "counting principles" could have a variety of interpretations but with regard to syllabus content for Maths SL & HL it basically includes the multiplication rule for counting*, factorial notation, combinations and - for HL only - permutations. For SL and the Sequences & Series; Binomial Theorem unit, it is not necessary to spend a great deal of time on counting principles. SL students need to be familiar with factorial notation so that they can understand the formula for combinations (binomial coefficients). It is expected that SL students can compute binomial coefficients by using both the formula for and their GDC. This skill will be very useful with binomial probability distributions (syllabus section 5.8) later in the course. HL students need to spend more time on counting principles, but this should be covered in the Counting Principles; Binomial Theorem; Induction unit.

* multiplication rule for counting (or, fundamental counting principle): If there are m ways an event can occur followed by n ways a second event can occur, then there are a total of m×n ways that the two can occur - and the idea can be extended to more than two events.
The rule can be very useful in other areas - such as in probability with computing the size of a sample space.