I am so sick of hearing the comment "P3 needs a way to directly control my allies! I keep dying because I can't control my allies!" that I decided to make this quick and easy guide to doing just that in Persona 3. Because you can, and it's very easy to do.
On Minato's turn, select the Tactics chamber on the battle menu. Press X. You will see a list of possible commands. What follows are their names and effects;
Act Freely: This is the default option. Each character will act according to their own set values and will try to take the best possible advantage of their inherent skillset. Most of the time, this option is sufficient.
Heal/Support: The ally will prioritize healing and support spells over any kind of offensive maneuver. If anyone on your team is even slightly hurt and the character under this command has a healing spell, they will use it. If everyone is sufficiently healthy, the character will attempt to use spells like Tarukaja and Sukunda to buff/debuff yours or your enemies' stats. If all support spells are active and everyone is healed to full, the character will prioritize normal attacks over other spells.
Note that this can force certain characters to do things that aren't normally possible/probable for them under Act Freely. Characters like Junpei and Koromaru who have no healing spells will attempt to use Medicine if you are hurt and their support spells have been cast.
Assign Target: The ally will prioritize attacks that will deal the most damage possible to the selected target. Generally, this means they will cast their strongest spell or ability on the selected target. Note that a character will generally not use skills that are known to repel, absorb, resist, or null unless all of their attack types do one of the above, in which case they will attack with whatever style of attack will cause the least personal harm.
Example: You Assign Target Ken to attack an enemy who is resistant to Pierce and Repels Lightning. Ken will always attempt to attack with his spear or will Vile Assault. If the targeted enemy Nulls Pierce, he will do the same thing, he will not Pass his turn under this condition.
Also note that when the targeted enemy dies, the ally will revert to Act Freely.
Conserve SP: Probably the most useless tactic, especially given that you have to earn it by beating the Priestess boss, the ally will prioritize skills that use HP and normal attacks over any kind of SP-using skill. This will force item-using characters to use them in lieu of spells of the same nature(Yukari will Anti-Charm instead of Charmdi, Aigis will use Medicine instead of Diarahan if she has it), and will force characters with both spells and HP abilities to always use their HP-Abilities. SP flows like water in P3, even on hard mode, and stopping the use of SP is often signing your death warrant, as normal attacks rarely win battles by themselves. Stay away from this.
Knock Down: Earned after defeating the Emperor and Empress, this tactic instructs allies to attack enemy weaknesses and to try to get critical hits to knock enemies down. This is probably the single most useful tactic in the game along with Heal/Support. Under most normal circumstances, allies will prioritize hitting knocked down enemies because it's a guaranteed hit and the enemy's defenses are lowered in that state. However, this means that your allies will rarely earn you All-Out attacks, which are the key to surviving for very long periods of time inside Tartarus. This tactic fixes that. Allies will use single-target spells to snipe individual enemies that are weak to the given spell being cast, in an attempt to knock them down and score extra turns. In the case of Kormaru and Ken, if an enemy is weak to Mudo or Hama they will simply attempt to outright kill all enemies weak to their element. If no enemies present are weak to the character's element, they will attempt a normal attack or HP ability with the highest critical hit chance in order to try to score a crit and knock down an enemy. If all enemies present are immune to criticals or to the character's attack type, they will pass their turn. If all enemies are already knocked down and for some reason you didn't make an all-out attack, the ally under this tactic will pass their turn.
Full Assault: This tactic is learned after defeating Heirophant and Lovers during the story. This tactic will cause the selected ally to simply choose the spell that will cause the most damage to the enemy group, and they will cast it. Under no circumstances will the character do anything other than attack. Even if an enemy Repels all their attack types, the character will continue their assault(And they will probably get killed too). However, if the enemy party contains a mix of resistances, the ally will refrain from doing things that will hurt them until the only option is an attack that will hurt them.
Example: Koromaru is under Full Assault. There is one enemy who is weak to Fire and another who Repels Fire, Slash, and Mudo(Koro's three elements). Even though technically Maragidyne would do the most possible damage, since it would hit two targets, it would hurt Koro, so he instead casts Agidyne on the first enemy. On the next turn, if the first enemy is dead, Koro will make a physical attack on the enemy, who will then repel the attack and hurt him. You should have changed the tactic!
Please note: The game operates under the assumption that status ailments are powerful spells. So if under this command, characters like Mitsuru might forgo casting spells like Bufudyne if an enemy resists Ice, and instead will attempt Marin Karin or Tantarafoo. This also happens under act freely, since the game assumes that an enemy under a status ailment is the same as a dead enemy.
Same Target: This tactic becomes available after you defeat Justice and Chariot. This command is essentially the same as Assign Target, except the ally will attack the exact same target that Minato attacks. If Minato attacks all enemies, the ally will attempt to do so as well. If the ally CANNOT do so, he will attack as if he were under the Act Freely command. This command does not end if the enemy attacked by Minato dies, the ally will simply Act Freely until Minato attacks a new target.
Attack Fallen: Another fairly useless tactic, and the last one you earn. You get it after defeating Hermit. Under this tactic, allies will attempt to hit enemies that have been knocked down, and will always use whatever will deal the absolute maximum damage to them. Honestly, this isn't much different then act freely, as most allies prioritize hitting knocked down enemies anyway, which is honestly something you don't want to do. Ignore this command.
Stand By: The humblest of orders, this command an ally to do pass his or her turn, performing no actions whatsoever. This is a lot more useful than it sounds. Utilized with other tactics, you can perform complex maneuvers, like having one ally knock an enemy down, and the following ally pass their turn, thereby forcing the knocked-down enemy to waste his turn getting up. You can also do this to prevent allies from doing things that would hurt them, like attacking an enemy who has cast Tetrakarn.
And last, but not least, the tactic that isn't really a tactic but kinda is:
Auto-Battle: By hitting Triangle at any point during battle, you can automatically set every single character to make a normal attack. By clicking Triangle again, you can cancel it to revert everybody back to their chosen commands. This can be a life-saver. If an enemy casts Tetrakarn, and you have one ally moving before Minato's turn, you can quickly press Triangle twice to force your ally to attack and get hit, nulling the Tetrakarn, then cancel the Auto-battle so that Minato can make an attack. You can also use this to force allies to stop casting spells, to force an ally who is Heal/Supporting to make an attack that would kill a final enemy, and any number of other useful tactics. Master the use of this.
Ken used tactics to wipe the floor with this shadow. If you use them to, you can do the same!
And there you have it. By using the Tactics chamber to set your allies actions for the turn, you can 100% predict every action that your allies take in battle, allowing you full control over every minute part of combat in Persona 3. Used in conjunction with Auto-Battle and the turn order viewer, you should never die against random shadows, not even on hard mode.