Hard Sudoku online
On Hard, obvious moves disappear early: you'll need to pencil in candidates across nearly the whole board and chain several logical techniques together to reach the solution.
Advanced solving, never guessing
A Hard Sudoku on Sudoku Rivals always has a single logical solution — you never need to guess — but reaching it requires combining several elimination techniques on the same cell or unit, not just applying one rule and moving on.
Common techniques on Hard
Hidden Pair — when two numbers can only go in the same two cells of a row, column, or box, even if those cells have other candidates pencilled in, those other candidates can be eliminated.
Alongside Naked Pair and Locked Candidates (already present on Medium), these techniques get combined several times in a single Hard game. The full explanation, with more detail, is at Sudoku Techniques.
Note: Hard is a difficulty, not the Extreme mode
Hard is a puzzle DIFFICULTY, describing how many techniques a board needs. It's separate from Extreme, which is a game MODE — the two describe different things and aren't the same setting.
Looking for something more approachable?
If you'd rather ease into it, try Medium Sudoku or Easy Sudoku.