Yu-Gi-Oh! Legacy of the Duelist

I find the best way to get a chain going is to Either use Quick play spell cards or Counter traps. When it asks if you wish to activate a card it will tell you if it will be part of a chain.

Quick play spells ( Circle with a lightning bolt ) :

Mystical Space Typhoon - Use this after any spell/trap activation to get a chain. You can even use it on itself if you wish to not destroy the card that was activated first, just make sure to use it after a spell/trap - not alone.

Scapegoat - Just use it after a Spell/trap/monster effect.

Poison of the Old Man - Just use it after a Spell/trap/monster effect. Also if you choose the second option to inflict 800 damage it will add towards your effect damage achievement.

While Counter traps are a lot more slow, and cannot be triggered right before the end of the game here are a few that work. I still suggest Quick play cards.

Solemn Judgment - Counters Summons, spells and traps for half of your life points. If you choose to counter a summon you may not get a chain, so if you are going for the chains only wait until it states that it is a chain.

Seven tools of the bandit or Magic jammer - Both of these have a simple job of countering Traps or Spells.

I was able to do this in one duel, you can play the first match v Kiba. You will need Mystic swordsman lv 6, Horus the black flame Dragon, and a spell caster for your monsters. You will need magical blast. And if you get multiple it helps, your swordsman will send their monster to the top of thror deck. This will lock them down and as well as allowing you to set up. Try to get horus lv 6 and use lv up. Now a spell caster will allow you to activate magical blast. Horus negates it and you can draw it instead. Two will set off a chain. Once you are done you can quit or surender.