Broken Base: The mobile entries tend to cause this, particularly in their native Japan, surprisingly. One side says they're a logical thing for Namco to pursue given the size of the market and that the apps can introduce more potential users to the real GE games, while their detractors tend to really lambast them for drawing resources away that could be used on the main titles. The abject failure of Online (which lasted all of 19 months) takes particular heat, and Resonant Ops being turn-based (in a franchise that prides itself on fast-paced action) also does it few favors.
BlitzHannibals. Take a Corrosive Hannibal, bleach its scales, and put the sucker on fast forward. If you thought the Hannibals were bad before, wait 'til you fight one that's twice as fast. Even worse, even its projectiles travel twice as fast.
The Arius Nova. It's the ungodly amalgamation of a Dyaus Pita, a Sariel, and an Arda Nova, with all the damaging moves and durability that all implies. Its wide-sweeping wing attacks are liable to put you in critical condition, if you're lucky. If not, kiss your ass goodbye.
Difficulty Spike: Whenever you make a transition from a storyline to another, there will be one. In Burst, and Resurrection, Difficulty 7 has a few breather levels, but kicks into full gear later, whilst Difficulty 11 follows suit.
The Venus may count for this, the human parts of her are quite sexy. Too bad the rest of her body kind of ruins it.
The same can be said of any of the other Aragami that take on some semblance of a humanoid female. Arda Nova, for example, would look completely human (and extremely sexy) were it not for the unusual skin coloration (magenta).
In early missions, the goddamn Chi-You and its goddamn damage-resistant legs and its goddamn fast-startup melee attacks that also let it move across the map quickly. Nowhere near Demonic Spider status since it remains killable and doesn't hit too hard, but still highly irritating.
Zygotes become a textbook example of this in mid-game level quests, taking precious seconds to kill even with a level-appropriate upgraded weapon, hitting you with various debuffs, and/or just distracting you from focusing on the boss.
The Borg Camlann line's tailspin and Arda Nova's combination attacks can be a pretty rude awakening if you can't see them coming.
The Arius Nova's ultimate attack which it extends its wings into huge blades that can reach the entire arena, swipes from two different directions from them and then finishes off with a sweeping Wave-Motion Gun, all of which are nigh impossible to dodge and can break through guards. Unless if the party is of four players, expect at least a couple members of the party to get knocked out by this attack if not an outright Total Party Kill.
Theiss Titillation Theory: The clothing design for a lot of the characters throughout the franchise, male and female, runs on this, though the women tend to be the most prominent examples. The lady "base commanders" in each major installment tend to really invoke the trope. Naturally, a lot of outfit options of this sort are available for your character, too.
For the Anime:
Base-Breaking Character: The protagonist of the anime, Lenka, has caused debate between those who like him more than Yuu, the canon protagonist of the games and most other adaptations. Lenka's detractors see him as a bland Stock Shōnen Hero compared to Yuu, who is caring, polite, intelligent, and cheerful while still being a total badass. However, Lenka isn't without his supporters, who like that he has an actual personality and backstory, in comparison to Yuu, who's a Vanilla Protagonist with no backstory or personality. Those who prefer Yuu tend to be those who have read the manga and light novels, where most of his actual characterization comes from, while those who mainly play the games or were introduced to the series by the anime lean more towards Lenka.
Fan Nickname: "Budget Eater" due to the high production values ufotable is putting into it, as well as the infamous episode delays detailed below. Alternately, there's also "Limited Budget Works," considering this anime started airing only weeks after ufotable's Fate/stay night [Unlimited Blade Works] which itself had the nickname of "Unlimited Budget Works" due to the incredible production values put into it, the joke being that UBW ate all of ufotable's budget and God Eater has to make do with the scraps left behind.