What is the process of filing a complaint against our neighbor (absentee landlord) due to colossal ficus taking over side yard?

Where is the boundary line between your properties? You can simply go ahead and trim any part of the tree/bush that protrudes over your property line without any notice or consent of the adjoining owner or official municipal approvals. If the trunk of the tree is on your side of the line, you can cut it down entirely.
If you are going to do anything like this, make sure you have a surveyor come out to stake and and flag the actual boundaries based on deeds and maps.

If the tree is intruding onto your side of the property line, then you can trim it as needed, including cutting the roots. But be careful doing this. You could end up liable for damaging or killing the tree - up to 3x the value of the tree. You may want to hire an arborist to make sure it is done without harm to the tree. Certain trees are protected (I don't think Ficus trees are on the list) so you may want to check with your city before doing anything.

you can sue your neighbor for trespass and/or nuisance. you can also try the administrative route.

Messrs. Spirtos and Lebowitz have provided you sound advice. I would recommend the letter before you take action so as to have a record of your complaint, in case the landlord tries to make a claim against you. Believe it or not, there is a whole regime about "tree law" in this state that you do not want to run afoul of. That is another good reason to have an attorney familiar with these issues to draft a letter on your behalf to the landlord explaining the issue and to advise you on how to proceed. I know, it seems ridiculous to involve lawyers over overgrown shrubbery, but I have personally witnessed these types of cases get very contentious and involve lawyers and courts and all sorts of madness. So, before you wade into that, consult knowledgeable counsel.
Michel & Associates, PC