Here's an example on how to budget clear Machina of Destruction (Aigon, robot trial) using a zero TMR, zero rainbow team:
Team I used:
Warrior of Light -- AoE cover and SPR breaking. Do not use taunts until the left arm is permanently dead.
Soleil -- geared to have the highest ATK on the team so the arm blast hits her every round. Dances for SPR before she dies.
Vanille -- gives re-raise on Soleil every round until the left arm is permadead, then she's just kind of there.
Roselia -- primary healer with triplecast white. She also does dispels (from an esper) when the boss buffs himself.
Beach Time Fina -- mana regen and DEF buff for the team, also backup healer/raiser if things go bad
friend Emperor -- enhanced, deals all the damages with ramping up Fires from Below +2
For the first phase, kill the left arm 10 times. This is the slow and boring way, but it's a lot safer than bursting the body down (and if you have the units to burst the body down you don't need a budget guide). Keep re-raise on your unit dedicated to taking the arm burst (will hit the highest ATK unit on the team unless it's taunted). If you're using Vanille for re-raise, keep in mind her re-raise brings back the unit at only 30% health, so you need your arm tanker geared with super high HP so they don't die again after the re-raise from the genocide beam. If you have a stronger re-raise like Ayaka, Prishe, Grim Lord Sakura, etc etc then use that instead.
When the right arm casts atk/mag buffs (every 4th turn) dispel it with off the main body first, then the right arm. Don't waste time dispelling the left arm because it's going to OTK a unit with or without the atk buff. When the left arm is finally dead 10 times, kill the right arm three times. Keep in mind that after the right arm dies once, it upgrades Aigon's main body to do genocide beam twice a turn instead of once a turn, so be sure to never kill the right arm at all until the left arm is permanently dead.
When both arms are dead for good, start working on the body. At 70% the boss will emote "The light is concentrating" which is a warning that next turn will be a super nuke on your team. If you hit him with a water attack while he's charging, it will reduce his super attack's damage by half, so be sure to do that. Don't ever use water except to interrupt his charge up attack, because after being hit 3 times with water (in total) he counters with another super nuke.
A decently geared enhanced Emperor friend will take off like 40% of an arm's life per cast of Fires from Below+2 after it ramps to 10 stacks. He's a better option than Blossom Sage Sakura because both arms are 50% resistant to lightning.