The fastest way to Elite in combat in the current version (as of 20th October 2018) is to kill Thargoid scouts because they are all elite combat rank. As with anything in this game a little preparation and knowledge is required.
Kit your ship with AX multi cannons, decontamination limpets and repair limpets. I'm using a Krait with 3 size 3 turreted ax multi's and 2 fixed beams. I have a xeno scanner but it is not essential it will tell you the scouts health. No engineering required on anything.
Each week eagle eye identifies sectors of interest to the Thargoids. So to find scouts follow the link below and scroll to the bottom. Go to a sector that has a station listed as a target. Now just cruise around the system slowly and look for USS's. You will easily find "Non Human" threat 3 or 4 in abundance if you are in the right system.
None of the work on this site is mine. All credit goes to their contributors. https://canonn.science/codex/eagle-eye-installations/
Threat 3 has 2 or 3 marauder scouts. Threat 4 will nearly always have 2 human ships and 4 or 5 marauder scouts. Occasionally there are upwards of 7 and all types of scouts (incidentally this is the same as a threat 5) this is much harder so its your call to stay or leave early.
When a scout is going to blow it make a a "honking scream" noise try to avoid flying through the cloud of bug snot when it does or you will take caustic damage but during the fight you might still get it. Don't panic. Kill the scouts. Stop and fire of a decontamination limpet then repair yourself. Now just go back into super cruise and find another.
You get 10,000 in combat bonds per scout so your not going to get rich but it will cover the bills and leave you some profit.
Its taking me 5 to 6 scouts to get 1% at dangerous.