I wouldn't; not my style to wholesale copy existing characters. If I was, I'd probably struggle to do so at 3rd level just because of the sheer amount of multiclassing you need to do to get it right. You need to start Rogue then go into Artificer for 3 levels to get Armorer and use the lighter version of the armor which doesn't impact stealth. Artificer's "magic" is flavored as gadgetry, which fits Batman better than a Fighter.
Stat-wise, I'd go 16 INT, 16 WIS, 14 CON, 14 DEX, 12 STR, 10 CHA.
For your 1st level feat (provided you opt to go Variant Human), I'd reccomend Skilled, Prodigy, or Observant.
Skilled will get you proficiency in 10 of the 18 skills right out of the gate, Prodigy gets you an extra language, tool, and skill proficiency as well as an expertise at 1st level, and Observant improves the detective angle.
If you go skilled, I'd say the most important skills are as follows, in order: Investigation/Perception (tied), Stealth, Intimidation, Deception (To keep up your alter ego), Acrobatics, Insight, History(this and Insight for his seemingly bottomless wealth of knowledge) Sleight of Hand, Athletics, anything else.
Your first ASI (5th level if you go Rougue 1/Artificer 4) should go to either INT (For your gadgets), WIS (For detective work), or DEX(For mobility in skill checks). Alternatively, grab one of the feats above you didn't take at 1st.
As for Rogue, go into Inquisitive when you get the chance for all the bonuses it gets you at 3rd. They're very batman-esque, with the inability to roll less than 8 on Insight checks to pick up lies, Bonus Action skill checks for spotting hiding creatures and hidden clues, and the ability to counter any foe in battle just like the bat.
You don't need more than 3 levels of Artificer, but you could go up to 5 for Extra Attack or even all the way to 7th to get Flash of Genius to really be the smartest man in the room.