At start, place prince on bridge.
When the left bandit starts taking damage from green slime (1 hit), place Camilla at the lower ranged spot between bandit and Prince.
When prince starts tanking second slime, place Iris at far left ranged spot, left of bandit.
Place Roy at ranged just above prince. Will kill first slime before second passes prince. Don't worry about the gobs that get through to the soldier, he'll mop up no problems.
Use hector to tank third slime at melee spot at crossroads (just left of prince) for one hit and withdraw just before second hits him and before either healer wastes a heal cycle on him (this is the crucial part, may take a couple tries to get right). This buys Roy enough time to nuke 2nd slime before 3rd passes prince.
Place iron HA at crossroads to tank ogre. [highlight]As soon as third slime is dead, withdraw Roy, place iron mage to the direct right of Iris. As soon as the slime the bandit is tanking is dead, withdraw iron mage, withdraw Iris, place twin archers firing on ogre. Will kill ogre before far right soldier dies of poison (barely). [/highlight] (Found better solution, see edit below)
Edit: Just watched a nico video of almost the same setup, but the end gives more breathing room for error: after third slime is dead, withdraw heavy armor, let it walk up to prince, who does far more damage, and place archer to finish it much quicker.