While these may be the way it is done out there - a LOT of it is overkill for the work we do with the equipment we handle.
Some of the good practices - keeping the iron tip tinned, using the ideal quantity of solder for a joint, care in tinning the cable, et al.
Some of the things not really needed for what we work with - frequent cleaning procedures with kimwipes - the soldering iron tip, the solder itself and multiple cleans of the job work (the item being soldered)...
Having said this - a lot depends on exactly what is the job at hand... (if one is doing SMD IC replcements - a lot of what is in the video applies. if one is just doing XLR connectors - no...)
As for your predicament - the information is not enough to provide a sensible remedy.
I would want to know:
Which Hakko unit?
How old is the tip?
What solder are you using/how old is it/how was it stored? Need to know composition and gauge
Did you clean and tin the tip before attempting anything at all?
Did you use a liquid flux from a flux pen or a syringe before trying to melt the existing solder junction?
So many questions...
TO Dalton: OF COURSE the real good stuff is STILL available. I wonder why you say it isn't.