Falkow's single player mission level 5 was really tough to beat. Props to the developers for putting up such a challenging mission. It took me several tries but I was finally able to find the right combination to beat Galdirea.
I start out with Carbuncle then Pucera. After that, make sure that the shield requirement of level 5 Refess will trigger. Then, plant Refugee Citizen to get rid of Galdirea's grims. Then, try to get Limier followed by Stronghold. Then use Turn to Dust and Chaos Absorption to try and thin out the opponent's deck. Simulacrum helps in trying to match the opponent's troops modified HP while getting rid of a card if the HP is less than or equal to zero. And if you still haven't zeroed out the cards in the deck, then speed it up with Magma Golem as another shield on the frontline.
For the SS lineup, Annette is really helpful in setting one unit of opponent's troops to max HP of zero. And you then add that HP to Pucera. The second one, you can add to Limier to prolong his presence on the field. The rest of the SS are worth 3 LP, hopefully enough to last Galdirea's assault on your LP. (Cause she gets to hit it for free every other turn or so).
Galdirea will also send one random grim from your deck out of the game. I tried using Mirelia to recover these but it just doesn't work. And the second SS of Galdirea prevents level 4 and above cards for a couple of turns so it's best to keep your units and cards at level three and below.
Hope this helps out other players who are struggling with that mission. Good luck!
