Have a look at
Keepass2Android Password Safe. I keep the data file on Drive and all my devices (a few phones, a PC, a laptop) use the same file. That way, all my passwords are always available (never use the same password on different sites) and I only have to remember one, so it can be a pretty strong one.
As for forgetting one, unless the site has a "Forgot my password" link, there's usually nothing you can do but think hard.