The list is arranged by rows, followed by the column number, for easy reference.
First 4 skills (H skills) need to be activated by spam clicking the shopkeeper

List of spells you'll need
1. Fulfilment
2. Quartet
3. Tornado
4. Glasses (either glasses works fine)
5. Monotone
6. Duplicate
7. Infinity
8. Barrier
9. Double barrier
10. Gift
11. Reflow

Also you'll need to eventually max out the HP for some of the achievements

Basic combos that I'll repeat quite often, skip if you would like to figure on your own
Fulfillment + quartet

1. Fulfillment to instantly get 50 MP regardless of rules
2. Quartet gives 4 of the "1" cards, which allows you to continue combos as well as draw more cards

Adding Tornado
For objectives that has more than "1" in its requirements, it'll reduce it to "1"

1. Use once per objective
2. When combined with Fullfillment + Quartet combo, you'll have at least 3 free draws at the start while clearing 3 objectives

Monotone/reflow
Additional QoL skills that allows you to continue combos and/or draw cards

1. Nonstop busting, nonstop lusting - Play a total of 100 cards

2. Those glasses are the real deal - Equip H skills
Method:
Unlock H skills by poking Shopkeeper, purchase and equip any of the glasses

3. Warm combo - Make a combo of 20

4. You have no excuses - Poke her crotch

5. Babe! - Play a total of 500 cards

6. Hoichi the one ear – Play a curse card 5 times in a single chapter
Method:
Use fulfilment + quartet to activate draws for higher chances of curses appearing, try to complete in 1 turn to complete 1 HP achievement too

7. Overload – Make a combo of 50
Method:
Use fulfilment + quartet and monotone when there’s consecutive numbers or no playable cards available

8. At home, but with a swimsuit – Poke Konoha

9. You have cleared Chapter 1 – Clear chapter 1 of Ikari

10. I was so stupid… – Clear chapter 1 of Mare

11. Little star – Clear chapter 1 of Roche

12. It’s not that complicated yet, but… – Clear chapter 1 of Troze

13. Total grasp of poker – Clear chapter 1 of Kurousa

14. It’s easy! – Clear chapter 1 of Leticia

15. Calm and collected – Clear chapter 1 of Konoha

1. Knife and lamp – Equip skills of all categories

2. T . T . K – Clear a chapter 2 within 2 turn
Method:
Fulfilment + Quartet + Tornado

3. The way of the seeker – Use Cutout to get ‘1’ and ‘1’
Method:
use Cutout on ‘1’, equip Quartet for guarantee draw

4. Tough guy – Reach 100 Health or more

5. Give me the back pocket – Activate an H skill

6. Eh… Perv! – Watch a scene of Troze

7. First time – watch 1 scene

8. You’re finally showing what you’re made of – Wach all the scenes of Mare

9. From tomorrow on I’ll take care of the place – Clear chapter 2 of Ikari

10. How are you this good – Clear chapter 4 of Mare

11. Chrono driver – Clear chapter 4 of Roche

12. I’m about to lose my mind – Clear chapter 4 of Troze

13. Clever strategy – Clear chapter 4 of Kurousa

14. Mental calculation are a pain – Clear chapter 4 of Leticia

15. The fox of the sweet tea – Clear chapter 4 of Konoha

1. Y-you’re alive! – get to 1 heath at the beginning of the turn
Method:
Use Fulfilment + Quartet + monotone in any Konoha stage
keep drawing cards + triggering curses

2. You’re too hasty – press the end turn button again while it's activated,
Method:
just smash that button

3. No, not now! – Restart

4. I love ◇ cards so much! – use square in every turn of a Roche Chapter
Method:
Roche Chapter 3, Fulfillment + infinity to get 2 ◇ per turn, play both ◇ cards consecutively and end turn for 2 turns

5. Omniscient – Get 10 or more cards in your hand
Method:
Fulfilment then Quartet x3

6. Full operation brain – draw all the cards in the deck in Troze’s stage
Method:
Fulfilment + quartet + monotone

7. Polygamy – watch 20 scenes

8. Experienced – watched 10 scenes

9. Major customer – Play a total of 200 turns

10. I wasn’t paying attention – Clear chapter 5 of Mare

11. Peace breaker – Clear chapter 5 of Roche

12. The genius of card games – Clear chapter 5 of Troze

13. Professional – Clear chapter 5 of Kurousa

14. I’ve added a whole year – Clear chapter 5 of Leticia

15. Horny for love – Clear chapter 5 of Konoha

1. I wonder what’s this – Right click for help/description

2. All bullets fire! – use 4 skills in 1 turn
Method:
Fulfillment + 3 low MP skills

3. Clear a chapter without using skills
Method:
Personally I chose Leticia Chapter 1 as busting the counter cannot damage you below 1HP, and combos stuns her, allowing you to end turn and try again.

4. If you don’t have a value. You don’t have a 0!?
Method:
Any Roche chapter. Fulfillment for MP, active ◇ ability, use blaze

5. Easy-peasy – A total of 10 objectives were achieved

6. Customer – Play a total of 10 turns

7. Cheating at playing cards – Make 5 of a kind
Method:
Fulfillment + quartet, click five ‘1’s and end turn

8. You’re a pervert but you’re good at this game… – Watch all the scenes of Troze

9. Well, you’ve been good – Clear chapters of Ikari

10. I have lost… – Clear chapters of Mare

11. Ahh, you’ve defeated me! ♡ – Clear chapters of Roche

12. I guess it’s okay if it’s with you… – Clear chapters of Troze

13. It’s my first defeat…! – Clear chapters of Kurousa

14. You are too good adding up! – Clear chapters of Leticia

15. I love you, Mister ♡ – Clear chapters of Konoha

1. Your odds to keep the combo going… are pretty high! – Play ◇ card as the last card in your hand

2. Taking a liking to fairies – Poke pirika (fairy in equipment tab)

3. Don’t take charity – Clear a chapter without additional draws except from deck
Method:
Play Roche Chapter 4, Fulfillment + Tornado, then play any card

4. Smooth sailing – Clear total of 5 chapters

5. Spell out – Draw all the cards in the deck
Method:
Fulfillment + Quartet + Monotone, Reflow is also useful here, best to attempt in Roche chapter using ◇ cards

6. Great to see you again – Buy a total of 10 items

7. Hmmm, this seems like a loss – Restart when Predicted damage is more than current HP

8. Restart – Restart without making any moves

9. I hate this outfit the most – Watch all the scenes of Kurousa

10. Bomb bad beat – lose with a hand better than Flush
Method:
when opponent’s happy, make a pair (not ‘1’s) and use Fulfillment + Quartet to make a Full house with three ‘1’s, end turn and hope you lose that round

11. Platinum member – Buy a total of 25 items

12. The master of repeating skills – use field effects 5 times in 1 turn
Method:
Troze chapter 5, bring fulfilment + Quartet + monotone to keep combo in the same turn
Use “count up/down” to get “4/8” cards, play “10” and use ability (10MP) on “6/2” cards to get “4/8” cards.

13. You’re being very pushy… – Watch all the scenes of Leticia

14. Cardcaptor – Purify at least 5 curse cards in a single chapter
Method:
Fulfillment + Quartet + monotone to keep drawing for curses, make sure to get purify card before using monotone since purify needs different color to obtain it

15. The fastest best moment – Make a combo of 40
Method:
Fulfillment + quartet + monotone

1. Balloonfish – Play a total of 1000 cards

2. Warming body – Poke Roche

3. Victory of endurance – Clear a chapter with more than 10 turns

4. Charity hasn’t been given – Clear Mare’s chapter without using cutout?
Method:
Play Mare Chapter 1, bring Fulfillment + quartet + Tornado,
Use Fulfillment + Tornado and playing any card for each objective X3, use quartet to maintain combo/draw more cards at any time

5. Jostle – Poke Pirika (fairy in equipment tab) 30 times

6. I like your belly – Poke the shopkeeper

7. I don’t want ◇ cards – Clear Roche’s chapter without playing ◇ cards

8. Broad forehead – Poke Leticia

9. Please treat me well forever – Watch all the scenes of Konoha

10. I’ll pour some salt for you – Play a purification card
Method:
play a card with +/- 2 value of different color to get purification card

11. A-All… bullets fire! – Use 12 skills in 1 turn
Method:
Fulfillment + Quartet + monotone + reflow
skip a turn to get max MP before using the skills, spam combos to keep drawing while using the skills, use reflow last

12. The star of speed – Clear a chapter without playing more than 15 cards
Method:
Same as achievement 14 (All according to the plan)

13. Effective strategy – Clear a chapter without playing more than 10 cards
Method:
Same as achievement 14 (All according to the plan)

14. All according to the plan – Clear a chapter without playing more than 7 cards
Method:
bring Fulfillment + Tornado,
play Troze Chapter 5, use both skill and play any card to complete in 1 turn

15. Detailed analysis – A total of 25 objective were achieved

1. Game over – Get defeated

2. There should have been 1 here – Delete a card using ‘Count down’
Method:
use ‘Count down’ on a ‘1’ card

3. Just caressing for now – Poke Ikari

4. 30 practiced games – Clear a total of 30 chapters

5. Perfect game – Clear a chapter without taking any damage
Method:
bring Fulfillment + Tornado,
play Troze Chapter 5, use both skill and play any card to complete in 1 turn

6. Arrest for touching – Poke Kurousa

7. So you are a pervert – Watch a scene of Leticia

8. Pervert! – watch a scene of Mare

9. One turn kill – Clear a chapter within 1 turn
Method:
Bring Fulfillment + Tornado,
play Troze Chapter 5, use both skill and play any card to complete in 1 turn

10. Looking how you play the cards – Make a combo of 5
Method:
bring Fullfillment + quartet,
using both skills should give enough to make combos

11. You’re so naughty – Watch a scene of Roche

12. The inspiration of a genius – A total of 50 objectives were achieved

13. No way it’s a combo of 3000 – Play a total of 3000 cards

14. It was too long- Clear a chapter by playing 50 or more cards
Method:
Method: Easiest on Roche chapter 3, bring Fulfillment + Quartet + Monotone + Infinity,
use quartet/monotone to draw as many cards as possible, 1st turn use fulfilment + quartet x2 to increase Max Cards to 50, use infinity to use ability x2 to clear objective each turn. Play last ◇ X2 only at the end when the entire deck has been played

15. Rollback – Restart a total of 10 times

1. Regular customer – Play a total of 50 turns

2. Defeating in progress – Clear a total of 10 chapters

3. Time travel – Restart 10 times without making any moves

4. Oh no! – Play a curse card immediately (start of chapter)

5. It came out a lot – Make a combo of 10
Method:
Fullfillment + quartet, using both skills should give enough to make combos

6. Thank you very much! ♡ - Buy something at the shop

7. I can see everything – Win after raising with only 1 pair
Method:
Fulfillment + Reflow + duplicate, Play Kurousa chapter 3 and watch for her expression to be bad, use reflow up to 3 times if there’s no ‘10’ card, then use duplicate on the highest card you have to form a pair and end turn

8. Insolvency – get defeated 10 times

9. Precious intimacy – Watch a scene of Konoha

10. Fully equipped – Reach 200 Health or more

11. I’ve enjoyed it to the fullest ♡ - Clear all Roche’s chapters with H skills activated

12. Why would I come back for more training – Clear all Ikari’s chapters with H skills activated

13. What…! You have a pair of perverted glasses! – Clear all Leticia’s chapters with H skills activated

14. No way! You’ve been watching me all this time…!? – Clear all of Mare’s chapters with H skills activated

15. Amazing! It’s pretty amazing! Clear all Konoha’s chapters with H skills activated

1. Unfair split – use cutout to form "10" cards
Method:
bring fulfilment + twenty,
use “cutout” on the “20” card to get “10” cards

2. Ughh…! – Watch a scene of Kurousa

3. Here is almost sexual harassment – Poke Mare

4. Bad flow – Fold 5 times in a row (will survive if done at start of chapter)

5. Heavy customer – Play a total of 100 turns

6. Why are you…? – Watch a scene of Ikari

7. It can’t be helped – watch all the scenes of Ikari

8. Dry and hard – Reach 150 health or more

9. Colorful dance – Use reflow to replace 5 or more cards at the same time
Method:
bring fulfilment + Quartet + Reflow,
use Quartet 3 times to get at least 14 cards then use Reflow

10. … Wait, those glasses are… Eh!? – Clear all Troze’s chapters with H skills activated

11. Hey, wait! – Force a turn end with playable cards in hand
Method:
Fulfillment + quartet,
use quartet on any Flare chapter without playing any cards, wait for the timer to end

12. High temperature high voltage diamond – Convert 3 pieces of soot at the same time by using furnace
Method:
Bring Fulfillment + quartet,
use Quartet on any Flare chapter, then immediately play a card other than “1”, which will all turn to soot after, then use special ability

13. Burnt to a crisp – Soot a total of 30 cards
Method:
Bring Fulfillment + quartet,
spam quartet and play any card to turn all “1”s to soot then restart chapter and repeat until completed

14. The victory of the suggestiveness – watch all scenes of Flare

15. Lewd fairy – watch a scene of Flare

1. I’m coming in a bit! ♡ - Make a girl climax in Free Touch mode
Method:
Shopkeeper and Pirika should be unlocked at the start, keep clicking them in the mode

2. Get a huge fortune – Get more than 10000 coins

3. Defense mode on – Allow 2 barrier frames
Method:
Bring Barrier + Double barrier + Gift + Blaze,
skip 1st turn to get 25 MP, use Blaze on “7” or more (if none then restart chapter), use barrier, gift, then double barrier

4. No-hit no-run game – clear a chapter 9 times without taking any damage
Method:
Bring Fulfillment + Tornado,
play Troze Chapter 5, use both skill and play any card to complete in 1 turn

5. That’s what I should have used. Great… – use a skill that consumes 51MP or more
Method:
Bring fulfilment + double barrier + Blaze + gift,
use blaze to increase max MP, use gift then double barrier.

6. My ideal lolicon – Watch all the scenes of Roche

7. Let’s poke her – poke Troze

8. All-out game – Clear a chapter by playing 100 or more cards
Method:
Easiest on Roche chapter 3, Fulfillment + Quartet + Monotone + Infinity,
use quartet/monotone to draw as many cards as possible,
1st turn use fulfilment + quartet x2 to increase Max Cards to 50, use infinity to use ability x2 to clear objective each turn. Play ◇ X2 only at the END of each turn

9. … Huh? Then… I’m completely…naked! – Clear all of Kurousa’s chapters with H skills activated

10. Just safe – Reset the timer using Furnace with less than a second remaining
Method:
Bring fulfilment on any Flare chapter,
play any card and wait for timer to be almost up then use the special ability

11. End – Clear all the chapters of Flare

12. Challenger – Clear chapter 1 of Flare

13. The size of the palm – Poke Flare

14. Perfection mode – Clear all Flare’s chapters with H skills activated

15. Peak of the challenge – Clear Chapter 4 of Flare

It's been a long while since I've played the game and I'm not really active in the post in the discussion so I figured I'll just post a guide for either the method or my own interpretation of the achievement if the translation is awful. My methods may not work for you depending on your play style but it should give you a hint otherwise.