Actual tip: impossible to miss while playing the game. Just interact with another LEGO brick using O on the PlayStation controller

One of my favorite games of the year. Should really get this one without trying

Glitch: If you have the game installed and updated to the latest patch, you can delete the "game utility data" from the PS3, which reverts the game to its original, unpatched state (for disc). Disconnect from the internet, boot up the game. This will install the game data, but not the patch. Your existing save should still be there. From here, simply load up a training pack from the Batcave and obtain 3 stars. The Initiation DLC trophies will pop afterwards. 

Don't make my mistake where I tried to install the game for the first time without internet, which obviously wouldn't work as there was never any recognized DLC. Waste of about 40 minutes, oops! 

TL;DR step by step:

• Install the game WITH the latest patches.
• Copy or upload your save data to the cloud (not required, but to be safe)
• Delete "game utility data" or all data if digital.
• Disconnect / turn off your internet and reinstall the game
• Play to or complete another training pack with 3 stars
• Trophies GET

Glitch: If you have the game installed and updated to the latest patch, you can delete the "game utility data" from the PS3, which reverts the game to its original, unpatched state (for disc). Disconnect from the internet, boot up the game. This will install the game data, but not the patch. Your existing save should still be there. From here, simply load up a training pack from the Batcave and obtain 3 stars. The Initiation DLC trophies will pop afterwards. 

Don't make my mistake where I tried to install the game for the first time without internet, which obviously wouldn't work as there was never any recognized DLC. Waste of about 40 minutes, oops! 

TL;DR step by step:

• Install the game WITH the latest patches.
• Copy or upload your save data to the cloud (not required, but to be safe)
• Delete "game utility data" or all data if digital.
• Disconnect / turn off your internet and reinstall the game
• Play to or complete another training pack with 3 stars
• Trophies GET

Deathstroke Fight - No Hit:

Basically, the way I did this was by using the batclaw slam (L2 + triangle, then square) and then attacking to achieve a combo of 8. Once obtained, you can use (triangle + o) to use a takedown. If you hit him too many times consecutively, he will counter you with a move that doesn't have counter icons even on normal, and can be difficult to counter. In addition to the batclaw slams, I would occasionally jump over him and hit him just once.

After taking a bit of damage from him, he'll stun you, then jump at you and spam you with strikes, which you must spam counters in return. Then you'll be able to beat him down. The second phase should be treated in the same way, except if he hits you, you'll need to hit counter twice with good timing. Also, Deathstroke may attach a remote claw to you, and a propane tank will be launched towards you, which you will need to counter before impact. Then the same stun sequence will repeat and go into the final stage. Still keep the same tactic, but if he counters you, you will need to counter 3 times in response. Next, there is one final stun sequence before the fight ends. If you didn't fail a counter, you'll get this.

Thanks to TheManUtdFan for some source information.