How to defend in bad positions

Be Fearless. Don't fear opponents aggressive attack. Most attacks aren't perfectly calculated and you must find the flaws. Then win the game. It's similar to a Poker game. Raising bets don't mean necessarily he got a superior hand.

The best way to refute a sacrifice is to Accept it.

This might also be a good thing to consider, www.chessable.com/tactical-resources-creative-attack-defense/course/37740/ and it's free :)

Try to delay your opponent, then regroup

One of Steinitz's rules of strategy:

If in an inferior position, the defender should be ready to defend and make compromises, or take other measures, such as a desperate counterattack.

@ryan121 well said though i wouldn't always accept sacrifice...

i'll add that a position will only give its maximum potential to you if you truely believe in it. Resilience is key in chess really.
other tips from my head
- trading often helps. better to defend an inferior endgame than to be in a mating net.
- don't fear losing material, a safe position with a pawn or an exchange down is often better than equal material with a bad position.
- look for opportunities when the attacker goes off the path. this actually would happen quite often to me.

if you're ready to suffer through deep learning. buy Mark Dvoretsky's book attack and defence ( very advance material!)

@Sardoix I play Aggressive Attacks myself. I can evaluate by intuition if the Attack or.Sacrifice is sound. If I am low on time, instead of calculating, Accept the sacrifice quickly. Let my opponent prove me wrong. I have played hundreds.of sparring games with Junior 6 15 years ago. I've seen Winning by Force. At U2200 level, playerd still.make plenty of errors in evaluating.

Learning to spot defensive resources seem like one area where computer analysis is quite helpful. Analyze games where you lost to a mating attack, and see whether there was a defensive move that you missed. You might well find that there's a certain sort of idea that you don't consider properly, and should keep an eye out for in the future.

Kortschnoi, Fischer, Ulf Anderssen, Karpov, Capablanca, Steinitz, Carlsen, Anand (sometimes), Kramnik, etc...

Defence is just tactics for the most part. You must know the attacking patterns (Bc2, Qd3 or Qg5, Bh6 or W: Qh6 Ng5 B: P:h7, g6, f7) and avoid them at all costs or find tricky ways to counter them (f5 with Qc7 covering g7 or h7 for instance). Also don't be afraid of checks! Every check gives your King an opportunity to escape. USE IT!

Lichess added the new puzzle system, where you can solve defence puzzles only. That might be a good place to start.

@RamblinDave quite true, computers are really good at that
Thing is it's quite often disgusting to see the line which could have saved you. i mean those computer lines are sometimes just near impossible to find for us. but it's nice to know they exist :p

Keres has a useful chapter in Art of the Middle Game (Keres and Kotov) on defending difficult positions.