A tip: If you pause, and go to "Battlefield Information," you'll see a list of your allies. Pick one and it'll show you where they are on the map. If you scroll right, you'll see a list of the enemies. Pick one and it'll show you where they are on the map. If you scroll left, you'll see a list of keeps (including the Allied Base). Pick one and you'll see where it's at.
In your case, use it to check where Fi is. Follow her and fend off enemies around her until she continues moving to where she makes the soup and calls the whale, who'll then create a bridge, allowing you to move to the next part of the map.
Also, when an ally or enemy talks, you'll see a ripple on the map where they're located. When an ally is in trouble, finding them and touching them (they'll be surrounded by blue rings) will heal them instantly.
When bombchus are on the move, they're a blinking x moving along a dashed line on the map. That shows where they're heading. Defend them or destroy them accordingly.
If you capture keeps around the Allied Base, the Allied Base will last longer. Remember, defeat enough enemies in the keep to empty its red meter and reveal the captain, who upon defeat will turn the meter blue.
Often, you have to capture enough keeps or defeat enough enemy captains (highlighted white) to lure out the enemy commander -- he or she will open the gates to their lair, sending out a faction of troops for a counterattack, and that's when you can move in for the kill (or stop to defend against the incoming enemies, boosting your KO count, building special meter, collecting rupees and materials, etc).
Another tip: You don't have to pick up materials or rupees. They're all picked up automatically at the end of the mission.
Another tip:
If you hold the dash button, you'll automatically go into a run. You can then release it and you'll keep running.
Another tip: By collecting magic, you fill up the green meter on the left of the screen. Once full, tap the right shoulder button to go into Focus Energy. You'll break the enemy captain's guard, doing more chip damage; you'll rack up more rupees and materials from enemies; you'll be more resistant to knock-back, and faster all around. And if you use a special attack during Focus Energy, you'll instantly reveal the Weakpoint Gauge of an enemy captain. Once that gauge is depleted, you'll deal serious damage to them. Normally, you have to bait and sidestep their attacks to briefly reveal the gauge, so this is like a nifty shortcut.