Get your resolving effects FAQ out, kids! Just making sure I have my understanding of how a turn would go with Luke Skywalker, Red 5 if Admiral Raddus gave him Battering Assault +10.

"Replaces turn: This character can move up to double speed, then attack each adjacent target once at +10 Damage. Determine legal targets before making the first attack roll. Huge or smaller characters hit by this attack are pushed back 2 squares from this character. This movement does not provoke attacks of opportunity."

Flurry Attack (Whenever this character scores a critical hit, he can make 1 immediate extra attack)

Rolling Fire (On its turn, each time this character defeats an enemy by making an attack, with a save of 11, it can immediately move up to 2 squares and then make 1 attack against another enemy without provoking an attack of opportunity)

1. Luke declares Battering Assault, moves double his speed, and ends adjacent to 2 characters, determining those 2 as his legal targets (step 1 of resolving effects).

2. Luke declares Use the Force to make his first attack a natural 20, which defeats a 50 HP character.

3. The character is moved 2 squares away from Luke, as it is not removed until step 14.

4. Flurry Attack occurs immediately (step 10), which he uses against the 2nd adjacent character, which does not defeat it.

5. Luke successfully makes a save for Rolling Fire (step 13).

6. Luke moves 2 and is no longer adjacent to the original 2nd target.

7. Luke uses the attack from Rolling Fire against the original 2nd target, which does not defeat it.

8. The first defeated character is now removed from the board (step 14).

9. Return to step 2 and Luke can use his Battering Assault attack against the original 2nd target only if it is still a legal target. It does not need to be adjacent, as it was already determined to be a target at step 1.

Have I overlooked anything?

why would you have to check when making the attack?

Lightsaber sweep is very different ability, as it creates non-targeted attacks which is why you can lawnmower with it.

Using blaster barrage as a template (From the FAQ), you would check for all legal targets for battering charge before making any of them, and then make those attacks in whichever order you choose, and at the time you make a particular attack, the target has to be legal. In Luke's case, since he is a shooter, he wouldn't necessarily need to be adjacent.

However a character with twin for instance, will often times not be able to take advantage of twin if battering into more than one target, since with a battering you push the target away, and it would no longer be a legal target (someone else is adjacent). You do check for legal target for each part of a twin and if for some reason you are no longer a legal target (maybe a veers CE from WOTC trigger or a zombie leia respawn CE) you wouldn't get a twin.