[legolas]

I've circled the alkyl group in red because I'm struggling the most with it.

I'd appreciate if you can help me complete this.

Thank you.

[Archer]

You need to break it down into simpler components.



The highlighted section in your figure would be ethylcyclopentane (IUPAC) on its own but it is bonded to your chain so it has to be rearranged to have the suffix "yl"

What would the IUPAC nomenclature for the following be?

[discodermolide]

ChemDraw gives this as the ending ---------undecyl)-5-ethyl-1,1,2-trimethylcyclopentane.
so you just need to figure out the ---------bit. So take each substituent and name it and find out the numbering starting from the      )-5-ethyl-1,1,2-trimethylcyclopentane end.
Don't forget alphabetical order for the groups and try and obtain the lowest sum of the locants.